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'TY  OF  CALIFORNIA, 

OF  CIVIL  ENGINEER!  NO 
u*.EY.  CAUFOKNIA 


National  Tube  Company 


BOOK  OF  STANDARDS 

AND 

USEFUL  INFORMATION 


CONTAINING 


TABLES  OF  SIZES  AND 

OTHER  USEFUL  INFORMATION  PERTAINING 
TO  TUBULAR  GOODS 


THE  ENGINEERING  DATA  FOR  THIS  BOOK 

EDITED  BY 
PROF.   REID  T.   STEWART 


1872 

Price,  $1.00 
1902 


Engineering 
Library 

COPYRIGHT,    1902,   BY 

NATIONAL  TUBE  COMPANY 

PITTSBURGH,    PA. 


CENTRAL  BUREAU  OF  ENGRAVING 
NEW  YORK 


National  Tube  Company 

MANUFACTURERS  OF 

BLACK  AND  GALVANIZED 

WROUGHT  MERCHANT  PIPE 

Of  All  Kinds  in  Sizes  from  }i  to  30  inches. 

BOILER  TUBES 

OF  MILD  STEEL  AND  CHARCOAL  IRON 

For  Stationary,  Locomotive  and  Marine  Work. 

CASING,  TUBING  AND  DRIVE  PIPE 

FOR  WELL  PURPOSES. 

GAS  AND  OIL  LINE  PIPE. 

CYLINDERS, 

Lapwelded  and   Seamless,  tested  100  Ibs.  to  3,700  Ibs.,  for  Com- 
pressed Air,  Carbonic  Acid  Gas,  Anhydrous  Ammonia, 
Etc.,  Etc.,  Etc. 

WATER  AND  GAS  MAINS, 

CONVERSE  AND  MATHESON 
LEAD  JOINT  PIPE  FOR  MAINS. 

Seamless  Tubes, 
Shrapnel,  Projectiles  and  Miscellaneous  Forgings, 

800375 


National  Tube  Company 

WORKS  AT 

MCKEESPORT          .          .          .      PENNSYLVANIA 

PITTSBURGH 

MIDDLETOWN      . 

PHILADELPHIA  . 

CHESTER 

OIL  CITY 

ELLWOOD   CITY 

CHRISTY  PARK  . 

VERSAILLES 

WHEELING    . '  .        .  WEST  VIRGINIA 

YOUNGSTOWN OHIO 

WARREN         

SYRACUSE NEW  YORK 

COHOES     

NEW  CASTLE        ....   DELAWARE 


GENERAL  OFFICE 

FRICK  BUILDING,  PITTSBURGH,  PA. 


LOCAL  SALES  OFFICES 

HAVEMEYER  BUILDING  .  .  NEW  YORK  CITY,  N.  Y. 
420  CALIFORNIA  STREET  .  .  SAN  FRANCISCO,  CAL. 
267  SOUTH  FOURTH  STREET  .  .  PHILADELPHIA,  PA. 
WESTERN  UNION  BUILDING  .  .  .  CHICAGO,  ILL. 
THE  FRICK  BUILDING  ....  PITTSBURGH,  PA. 
NATIONAL  TUBE  WORKS  ....  ST.  LOUIS,  MO. 


FOREIGN  OFFICE 

DOCK  HOUSE,  BILLITER  STREET,  LONDON,  E.  C.,  ENG. 


TELEGRAPHIC  ADDRESS,  TUBULIFORM,  LONDON 


^PREFACE 


In  the  following  tables  of  Standard  dimen- 
sions of  Tubular  Goods,  it  has  been  our  aim  to 
group  together  in  one  book  all  of  the  dimensions 
and  data  pertaining  to  standards  as  manufac- 
tured by  National  Tube  Co.  at  this  date,  with 
the  object  of  making  this  book  a  practical  and 
valuable  aid  to  all  users  of  'Pipes,  Tubes,  etc. 
The  use  of  Tubular  Goods  has  become  so  ex- 
tensive that  a  great  variety  of  articles  necessary 
for  different  purposes  has  to  be  manufactured, 
and  a  large  amount  of  data  has  accumulated 
on  the  subject,  and  we  trust  that  our  effort  to 
put  this  before  the  public  in  a  compact  form 
•will  prove  of  *balue. 

We  have  also  taken  up  certain  subjects 
closely  related  to  the  use  of  pipes,  tubes,  etc., 
and  furnished  such  general  information  and 
engineering  data  pertaining  to  same,  as,  we 
think,  *h>ill  be  useful  and  appropriate  in  a  book 
of  this  kind,  vjith  the  idea  of  popularizing  such 
information  that  would  lead  to  the  intelligent 
application  of  tubular  goods  for  purposes  where 
engineering  skill  and  judgment  should  be  exercised. 
This  data  was  prepared  for  publication  by  Prof. 
cfyid  T.  Stewart  and  is  largely  compiled  from 
modern  welt-known  engineering  authorities  on 
the  subjects. 


TABLES 

OF 

STANDARD  DIMENSIONS 

OF 

Tubular  Goods 


AS  MANUFACTURED 
BY  THE 


NATIONAL  TUBE  Co. 


NATIONAL  TUBE  COMPANY. 


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National  Tube  Co.  Standard  Line  Pipe. 

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National  Tube  Co.  Standard  Drive  Pipe. 

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NATIONAL  TUBE  COMPANY.                       15 

STANDARD  DIMENSIONS  OF  COUPLINGS 

FOR 

STEAM,  GAS  AND  WATER  PIPE, 

BLACK  AND   GALVANIZED. 

Size  of 
Pipe. 
Nominal 
Inside 
Diameter 

Inside 
Diameter 
of 
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Outside 
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'     of 
Coupling 

Length 
of 
Coupling 

Thread 
per  Inch  of 
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Average 
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in  Pounds. 

Inches. 

Inches. 

Inches. 

Inches. 

# 

H 

if 

H 

27 

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7^ 

8T5^ 

4^ 

8 

11.270 

8 

8^ 

^ 

4^ 

8 

15.150 

9 

9iV 

10^ 

5^ 

8 

17.820 

10 

ioTv 

Utt 

6^ 

8 

27.700 

11 

HM 

12H 

6^ 

8 

33.250 

12 

12TV 

18# 

6^ 

8 

43.187 

13 

13H 

15TV 

6^ 

8 

49.280 

14 

14ff 

16^ 

6^ 

8 

63.270 

15 

15H 

17^ 

6^ 

8 

66.000 

(  «  - 

16                        NATIONAL  TUBE  COMPANY. 

STANDARD  DIMENSIONS  OF  COUPLINGS 

FOR 

REGULAR  CASING. 

Size  of 
Casing. 
Nominal 
Inside 
Diameter 

Inside 
Diameter 
of 
Coupling 

Outside 
Diameter 
of  . 
Coupling 

Length 
of 
Coupling 

.Thread 
per  Inch  of 
Screw. 

Average 
Weight 
of 
Coupling 
in  Lbs. 

Inches. 

Inches. 

Inches. 

Inches. 

llf 

\7/& 

2rV 

2^ 

14 

.90 

2 

%~$? 

2|| 

2$ 

14 

1.31 

2^ 

3^1. 

g2  9 

2$ 

14 

1.50 

2/^ 

2^T 

3  5 

2fy 

14 

1.62 

2% 

2H 

3fff 

2$ 

14 

1.75 

3 

8* 

3|^ 

3/4 

14 

2.62 

3^ 

41 

4 

3/^ 

14 

2.87 

319 

4j/ 

31^ 

14 

3.06 

3^ 

3!  7 

4K 

3/^ 

14 

2.25 

4 

4  ' 

4f| 

3^ 

14 

3.62 

4X 

4i^ 

5 

3^ 

14 

3.93 

4/^5 

444 

5A 

35*6 

14 

4.06 

5^ 

1 

sf! 

5|| 

4^ 

14 

4.93 

5.68 

5$ 

aft 

4/^ 

u&lly2 

5.93 
6.37 

6^ 

6.L5. 

7S 

4/^ 

14  &  11  ji 

7.93 

65*6 

651 

7|| 

4f^ 

14  &  ll/^ 

9.68 

7X 

7!! 

4^ 

14  &  11^ 

9.93 

735 

883 

51^ 

11^ 

14.00 

8// 

3^1 

93/ 

51^ 

ll/^ 

15.37 

8$A 

8?6 

yj>/ 

5/^ 

11  /^ 

15.93 

9^6 

9a/ 

1086 

11  /^ 

24.60 

10* 

10/ 

H>| 

6/^ 

11^ 

26.00 

1Q26 

\~\_7/. 

gi^$ 

11^ 

27.83 

11^ 

lifl 

\%7/ 

6/^ 

11^ 

29.75 

125^ 

^2al 

14 

6/^ 

11  M 

35.00 

13^ 

13f| 

15 

6/^ 

H>^ 

42.50 

14  /^ 

16  1/ 

gr^ 

UK 

50.00 

«# 

15* 

17/8 

6JS 

UK 

52.50 

NATIONAL  TUBE  COMPANY.                         17 

STANDARD  DIMENSIONS  OF  COUPLINGS 

FOR 

LINE  PIPE. 

Size  of 
Pipe, 
Nominal 
Inside 
Diameter 

Inside 
Diameter 
of 
Coupling 

Outside 
Diameter 
of 
Coupling 

Length 
of 
Coupling 

Thread 
per  Inch  of 
Screw. 

Average 
Weight 
of 
Coupling 
in  Pounds. 

Inches. 

Inches. 

Inches. 

Inches. 

X 

H 

fi 

ITB^ 

18 

.06 

H 

II 

u 

Itt 

18 

.17 

% 

If 

1* 

lit 

14 

.29 

X 

if 

1/8 

2A 

14 

.41 

\ 

Hi 

1# 

2A 

UK 

.64 

w 

IK 

2M 

3« 

UK 

1.10 

w 

in 

»A 

HI 

UK 

1.18 

2 

a* 

2^ 

3^ 

UK 

2.50 

2K 

3tt 

3TV 

3^ 

8 

3.12 

3 

3& 

4A 

3^ 

8 

3.85 

3K 

3^ 

4H 

4T\ 

8 

5.00 

4 

4& 

5T3ff 

4A 

8 

6.50 

4K 

4ff 

5^ 

4T3^ 

8 

7.70 

5 

5X 

Z& 

5^ 

8 

11.21 

6 

6TBTT 

ftt 

5^ 

8 

12.00 

7 

7« 

8H 

6^ 

8 

14.75 

8 

8tt 

9TV 

5^ 

8 

23.25 

9 

m 

10^ 

6>g 

8 

26.48 

10 

IOH 

HH 

6^ 

8 

29.50 

11 

11% 

12ii 

6^ 

8 

34.75 

12 

12TV 

13^ 

6^ 

8 

39.50 

18 

13H 

15TV 

6^ 

8 

46.00 

14 

14|| 

16TV 

6^ 

8 

59.75 

15 

15H 

17k 

6^ 

8 

62.25 

\i 

18                         NATIONAL  TUBE  COMPANY. 

STANDARD  DIMENSIONS  OF  COUPLINGS 

FOR 

DRIVE  PIPE. 

Size  of 
Pipe 
Nominal 
Inside 
Diameter 

Inside 
Diameter 
of 
Coupling 

Outside 
Diameter 
of 
Coupling 

Length 
of 
Coupling 

Thread 
per  Inch  of 
Screw. 

Average 
Weight  of 
Coupling 
in  Pounds. 

Inches. 

Inches 

Inches. 

Inches. 

2ii 

ll^i* 

1.10 

l/^ 

!%• 

2395 

gi| 

l\% 

1.18 

2 

JJC 

2% 

3'M 

\\\4> 

2.50 

gs? 

315 

3§i 

8 

3.12 

3" 

3J4 

^ts 

3% 

8 

3.85 

3&j 

3i5 

423 

4^3 

8 

5.00 

4 

4J4 

5^ 

4-3s 

8 

6.50 

4^4 

4% 

5% 

43 

8 

7.70 

5 

517 

gi£ 

5/^ 

8 

11.21 

0 

g_s 

71  3 

51^ 

8 

12.00 

7 

7*1 

41 

gix 

8 

14.75 

8 

gi  i 

9? 

6V^ 

8 

23.25 

9 

9j| 

§y& 

8 

2648 

10 

10% 

nil 

giz 

8 

29.50 

11 

11% 

gi^ 

8 

34.75 

12 

12  7jt 

13% 

giz 

8 

39.50 

13 

isle 

15rs 

gi^ 

8 

46.00 

14 

142? 

jg^ 

gi^ 

8 

59.75 

15 

15f! 

17W 

6^ 

8 

62.25 

STANDARD  DIMENSIONS  OF  COUPLINGS 

FOR 

TUBING. 

Size  of 
Tube 
Nominal 
Inside 
Diameter 

Inside 
Diameter 
of 
Coupling 

Outside 
Diameter 
of 
Coupling 

Length 
of 
Coupling 

Thread 
per  Inch  of 
Screw. 

Average 
Weight  of 
Coupling 
in  Pounds. 

Inches. 

Inches. 

Inches. 

Inches. 

1.10 

ji7 

J23 

2_9 

2ri 

11/4 

1.18 

2 

2 

2% 

39i 

11^ 

2.50 

0?9 

s2 

3% 

llifj 

3.12 

3 

g37^ 

41 

3^ 

H/^j 

3.85 

gix 

sii 

423 

4  ^ 

8 

5.00 

4 

4v 

gj5 

8 

6.50 

423 

gK/ 

8 

7.70 

5 

5J4 

6TI 

8 

11  21 

6 

rfl 

8 

12.00 

1  ;  n 

NATIONAL  TUBE  COMPANY.                       19 

SPECIAL  LIGHT  LAP-  WELDED  PIPE 

FITTED  WITH 

CAST  IRON  LUGGED  FLANGES. 

Shrunk  on,  Beaded  and  Expanded,  and  Finished  with  Bolts,  Nuts  and  Gaskets,  Complete. 

1A11  quotations  based  on  random  lengths,  16  to  18  feet.  Suitable  for  water  at  pressure  not  exceeding  80  Ibs 
per  square  inch.  For  compressed  air.  For  gas,  and  for  exhaust  steam.  (See  illustration,  page  25.) 

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Size  of  Gasket. 

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NATIONAL  TUBE  COMPANY.  25 


SPECIAL  LIGHT  LAP- WELDED  PIPE       LAP- WELDED  PUMP  COLUMNS 

Fit  ted  with  Cast  Iron  Lugged  Flanges.      Fitted  wltc2£i 


LAP-WELDED  PIPE  LAP-WELDED  PIPE 

Fitted  with  Cast  Iron  Collar  Flanges.       Fltted  with  Cast  Iron  Single  Riveted 

Flanges. 


LAP-WELDED  PIPE  LAP-WELDED  PIPE 

Fitted  with  CasUronDouble  Riveted         FiUed  whh  SoHd  Wdded  p,anges 


NATIONAL  TUBE  COMPANY. 


CAST  IRON 

THREADED 

FLANGES. 

Master  Steam  Fitters' 
Standard  Sizes* 

Bolting  for  Light  Pressures 

Not  Exceeding 
Seventy-Five  Pounds. 


Pipe 
Size. 

Outside 
Diameter 
of 
Flange. 

Thickness 
of  Face. 

Number 
of 
Bolts. 

Size  of 
Bolts. 

Bolt 
Hole 
Circle. 

Weight 
per  Pair 
in  Lbs. 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

2 

6 

% 

4   - 

% 

4^ 

8 

2</2 

7 

H 

4 

v* 

5j^ 

12 

3 

7^ 

# 

4 

% 

6 

14 

3^ 

Sy2 

If 

4 

y* 

7 

20 

4 

9 

11 

4 

% 

7^ 

24 

4K 

9X 

if 

8 

# 

7# 

25 

5 

10 

if 

8 

% 

8^ 

30 

6 

11 

1 

8 

% 

9K 

34 

7 

iStf 

IxV 

8 

% 

10^ 

46 

8 

18# 

i# 

8 

# 

11^ 

54 

9 

15 

i# 

12 

% 

13X 

66 

10 

16 

IT"* 

12 

x 

14X 

74 

12 

19 

i# 

12 

X 

17 

112 

14O.D. 

21 

1/8 

12 

H 

18# 

147 

15    " 

22^ 

1/8 

16 

# 

20 

162 

NATIONAL  TUBE  COMPANY. 


SPECIAL 

Steel  Lap -Welded  Pipe, 

FITTEI>    WITH 

CONVERSE    PATENT    LOCK   JOINT. 

(Cast  Iron  Hub.) 


SILVERTIN. 


SIZE. 

APPROXIMATE  WEIGHT. 

0.  D. 

Inches. 

Nearest 
B'g'm 
Wire 
Gauge. 

Plain 
Ends, 
per  foot. 
Ibs. 

Hub. 
Ibs. 

Lead, 
one  side. 
Ibs. 

Complete, 
per  foot. 
Ibs. 

2 

13 

1.91 

5 

1 

2.00 

3 

12 

3.33 

9 

2 

3.94 

4 

11 

4.89 

14 

2^ 

5.81 

5 

10 

6.85 

19 

3 

8.02 

6 

10 

8.26 

21 

4 

9.65 

7 

9 

10.65 

32 

5/2 

12.74 

8 

9 

12.21 

35 

7 

14.54 

9 

8^ 

14.58 

37^ 

?K 

17.08 

10 

8^ 

16.18 

41 

8 

18.90 

12 

7 

22.35 

58 

10 

26.13 

14 

7 

25.25 

73 

12 

30.00 

15 

W 

30.00 

85 

15 

36.40 

16 

5 

39.60 

132 

17# 

46.25 

18 

X 

47.00 

149 

30 

56.25 

20 

65.15 

217 

38 

78.50 

22 

u 

78.50 

280 

50 

96.00 

24 

y% 

93.50 

342 

58^ 

114.50 

26 

H 

102.00 

380 

70 

138.00 

28 

X 

110.00 

430 

85 

151.00 

30 

ft 

136.60 

475 

100 

168.60 

NATIONAL  TUBE  COMPANY. 


WEIGHTS  OF  FITTINGS. 
Converse  Joint, 

As  a  matter  of  convenience  and  to  give  an  idea  of  the 
average  weight  of  Converse  Patent  Lock  Joint  Fittings, 
we  submit  the  following  list  of  a  few  standard  patterns. 

All  ends  are  Converse  L/ock  Bells,  except  where  other- 
wise stated.  Bell  connections  for  cast  iron  pipe  are 
indicated  by  an  asterisk  (*) ;  bell  connections  for  threaded 
pipe,  by  a  single  dagger  (f). 


REDUCING  TEES. 


Size. 

Weight 
Ibs. 

Size. 

Weight 
Ibs. 

Size. 

Weight 
Ibs. 

3x2x2 

34 

6x5x5 

81 

14x14x10 

3x2x3 

30 

6x6x5 

97 

14x14x12 

3x3x2 

36 

7x4x7 

16xl6x  4 

330 

3x4x3 

35 

7x7x4 

'si 

16xl6x  6 

355 

4x2x4 

43 

7x5x7 

16xl6x  8 

4x3x2 

39 

7x7x5 

16x16x10 

4x4x2 

35 

7x6x7 

16x16x12 

4x3x4 

36 

7x7x6 

16x16x14 

4x4x3 

37 

7x6x6 

18xl8x  6 

4x3x3 

40 

8x4x8 

107 

18x18x10 

4x4x6 

55 

8x8x4 

91 

18x18x12 

5x3x5 

8x5x8 

117 

18x18x16 

5x5x3 

57 

8x8x5 

118 

20x20x  6 

5x4x5 

8x6x5 

100 

20x20x  8 

640 

5x5x4 

60 

8x6x8 

103 

20x20x10 

5x5x6 

70 

8x8x6 

97 

20x20x12 

6x3x3 

60 

8x6x6 

87 

20x20x14 

6x3x6 

60 

10x10x4 

118 

20x20x16 

6x4x5 

76 

10x10x5 

24x24x  6 

6x4x6 

68 

10x6x10 

24x24x  8 

6x6x3 

59 

10x10x6 

iii 

24x24x10 

6x6x4 

70 

10x10x8 

136 

24x24x12 

6x5x4 

79 

12x12x4 

161 

24x24x14 

6x4x4 

58 

12x12x6 

156 

24x24x16 

6x5x6 

12x12x8 

160 

NATIONAL  TUBE  COMPANY.                        29       • 

CONVERSE  JOINT  FITTINGS. 
CROSSES. 

SIZE. 

Weight' 
Ibf. 

SIZE. 

Weight 
Ibs. 

SIZE. 

Weight 
Ibs. 

2x2x2x2 
3x3x3x3 
4x4x4x4 
5x5x5x5 
6x6x6x6 

21 
39 

57 
71 
104 

8x  8x  8x  8 
10x10x10x10 
12x12x12x12 
14x14x14x14 
16x16x16x16 

156 
205 
306 

18x18x18x18 
20x20x20x20 
22x22x22x22 
24x24x24x24 

REDUCING    CROSSES. 

SIZE. 

Weight 
Ibf. 

SIZE. 

Weight 
Ibs. 

SIZE. 

Weight 
Ibs 

3x3x2x2 
3x2x3x2 
4x4x2x2 
4x4x3x3 
4x3x4x3 
5x5x3x3 
5x3x5x3 
5x5x4x4 
5x4x5x4 
5x5x5x4 
6x6x4x4 
6x6x3x3 
6x3x6x3 
6x6x5x5 
6x5x6x5 

'39 
46 
60 
50 

71 

'i\ 

77 
67 

120 
102 

6x  4x  6x  4 
6x  6x  6x  3 

8x  8x  4x  4 
8x  4x  8x  8 
8x  6x  8x  6 
8x  6x  4x  4 
8x  8x  6x  6 
8x  8x  5x  5 
lOxlOx  4x  4 
lOx  4xlOx  4 
lOxlOx  5x  5 
lOx  SxlOx  5 
lOxlOx  6x  6 
lOx  6xlOx  6 
lOxlOx  8x  8 

78 
103 
98 
131 
129 
132 
118 
127 
125 
123 
162 

166 
i98 

lOx  8xlOx  8 
12xl2x  6x  6 
12x  6xl2x  6 
12xl2x  8x  8 
12x  8xl2x  8 
12x10x12x10 
14x14x12x12 
16x16x10x10 
16x16x12x12 
18xl8x  6x  6 
18x18x10x10 
18x18x12x12 
20x20x  6x  6 
20x20x10x10 
20x20x16x16 

218 
166 

261 
646 

MISCELLANEOUS  CROSSES. 

SIZE. 

Weight 
Ibf. 

SIZE. 

Weight 
Ibf. 

SIZE. 

Weight 
Ibs. 

4x4x6x4 
6x5x6x4 
6x4x4x4 
6x4x6x3 

92 

110 
90 
93 

6x6x6x4 
6x6x6x3 

8x6x8x5 
8x4x8x8 

105 
103 
126 
131 

8x6x8x4 
8x4x6x6 

136 

Some  of  the  weights  in  these  tables  of  Converse  Joint  Fittings 
are  not  given  ;  the  reason  being  that  there  are  not  Standard  pat- 
terns for  the  sizes  where  weights  are  omitted,  and  the  patterns  of 
some  other  sizes  are  made  adaptable  for  same.    This  would  cause 
a  variation  in  weights,  and  for  this  reason  it  is  thought  best  to 
give  no  fixed  weights  for  fittings  so  manufactured. 
' 

30                         NATIONAL  TUBE  COMPANY. 

TEES, 

SIZE. 

Weight, 
Ibf. 

SIZE. 

Weight, 
Ibf. 

SIZE. 

Weight, 
Ibf. 

2x2x2 
3x3x3 
4x4x4 
5x5x5 
6x6x6 
7x7x7 

17 
29 
45 
56 
70 
84 

8x  8x  8 
9x  9x  9 
10x10x10 
12x12x12 
13x13x13 
14x14x14 

127 

178 
192 

359 

15x15x15 
16x16x16 
18x18x18 
20x20x20 
22x22x22 
24x24x24 

957 

MISCELLANEOUS  TEES. 

SIZE. 

Weight, 
Ibf. 

SIZE. 

Weight, 
Ibf. 

SIZE. 

Weight, 
Ibs. 

6x  5x  4 
lOx  4x10 
lOx  5x10 
lOx  6x  6 

79 

iio 

lOx  8x10 
10x10x12 
lOx  8x  8 
12x  6x12 

135 

182 

12x  8x12 
12x  8x  8 
14x12x14 
16x  8x16 

282 
600 

REDUCERS. 

SIZE. 

Weight, 
Ibf. 

SIZE. 

Weight, 
Ibf. 

SIZE. 

Weight, 
Ibf. 

3  to  2 
4  to  2 
4  to  3 
5  to  3 
5  to  4 
6  to  2 
6  to  3 
6  to  4 
6  to  5 
7  to  5 
8  to  3 
8  to  4 

27 
22 
27 
39 
36 
55 
36 
40 
46 
52 
60 
53 

8  to    5 
8  to    6 
10  to    4 
10  to    5 
10  to    6 
10  to    8 
12  to    5 
12  to    6 
12  to    8 
12  to  10 
13  to  12 
14  to  13 

70 
63 
90 
94 
94 
107 
154 
154 
138 

'90 

88 

16  fco  6 
16  to  8 
16  to  10 
16  to  12 
18  to  16 
20  to  12 
20  to  18 
20  to  16 
24  to  12 
24  to  18 
24  to  20 

295 

256 
256 

442 
395 
505 

608 

) 

NATIONAL  TUBE  COMPANY.          31 

ELLS. 

Wt. 

wt. 

Wt. 

SIZE. 

SIZE. 

SIZE. 

Ibs. 

Ibs. 

Ibs. 

2x2x90° 

12 

7x  7x45° 

14xl4x22i6 

2x2x60° 

7x  7x30° 

14x14x10° 

2x2x45° 

'9 

7x  7x224° 

39 

15x15x90° 

2x2x30° 

8 

7x  7x10° 

15x15x60° 

2x2x224° 

8x  8x90° 

95 

15x15x45° 

2x2x10° 

8x  8x60° 

71 

15x15x30° 

3x3x90° 

25 

8x  8x45° 

69 

15x15x224° 

3x3x60° 

8x  8x30° 

15x15x10° 

3x3x45° 

12 

8x  8x224° 

64 

16x16x90° 

420 

3x3x30° 

8x  8x10° 

50 

16x16x60° 

3x3x224° 

13 

10x10x90° 

148 

16x16x45° 

265 

3x3x10° 

10x10x60° 

16x16x30° 

4x4x90° 

32 

10x10x45° 

93 

16x16x224° 

4x4x60° 

25 

10x10x30° 

16x16x10° 

4x4x45° 
4x4x30° 

23 

17 

10x10x224° 
10x10x10° 

18x18x90° 
18x18x60° 

4x4x224° 

12x12x90° 

205 

18x18x45° 

4x4x10° 

12x12x60° 

18x18x30° 

5x5x90° 

41 

12x12x45° 

132 

18x18x224° 

5x5x60° 

12x12x30° 

108 

18x18x10° 

5x5x45° 

32 

12x12x224° 

112 

20x20x90° 

840 

5x5x30° 

12x12x10° 

95 

20x20x60° 

5x5x224° 

13x13x90° 

230 

20x20x45° 

5x5x10° 

13x13x60° 

20x20x30° 

620 

6x6x90° 

57 

13x13x45° 

20x20x224-° 

365 

6x6x60° 

48 

13x13x30° 

20x20x10° 

6x6x45° 
6x6x30° 

41 
39 

13x13x224° 
13x13x10° 

24x24x90° 
24x24x60° 

1143 

6x6x224° 

30 

14x14x90° 

247 

24x24x45° 

6x6x10° 

30 

14x14x60° 

24x24x30° 

7x7x90° 

72 

14x14x45° 

163 

24x24x224° 

550 

7x7x60° 

14x14x30° 

24x24x10° 

Y'S. 

SIZE. 

wt. 

SIZE. 

Wt. 

SIZE. 

Wt. 

Ibs. 

Ibs. 

Ibs. 

3x3x3 

33 

6x6x6 

123 

12x12x12 

350 

4x4x4 

70 

8x8x8 

180 

18x18x18 

1145 

5x5x5 

95 

10x10x10 

262 

20x20x20 

2400 

32                       NATIONAL  TUBE  COMPANY. 

PLUGS. 

SIZE. 

Wt. 

Ibs. 

SIZE. 

Wt. 
Ibs. 

SIZE. 

Wt. 
Ibs. 

2 

1 

6 

10 

10 

25 

3 

3 

7 

14 

12 

30 

4 

5 

8 

19 

14 

40 

5 

9 

9 

22 

16 

54 

MISCELLANEOUS. 

CROSSES. 

TEES. 

ELLS. 

SIZE. 

Wt. 
Ibs. 

SIZE. 

Wt. 
Ibs. 

SIZE. 

Wt. 

Ibs. 

3x3xlfxlf 

22 

2x  2  x  ff 

11 

6x  4fx90° 

70 

4x4x2fx2f 
4x4x6*x6* 

56 
124 

2x  2  xlif 
3x  3  xl  f 

11 
22 

6x  5fx90° 
12xl2fx60° 

65 

180 

4x4x4  x2f 

6x6x8*x8* 

75 
184 

3x  2fx3 
4x  4  x2  f 

43 

44 

REDUCERS. 

6x6x4x2f 

83 

5x  3  x2  f 

40 

SIZE. 

Wt.  ibs 

6x  6  x2  f 

97 

4    to    2f 

17 

10x10  x4i-- 

163 

12    to  12* 

247 

10x10  x7  •• 

165 

16    to  16* 

450 

4x  4  x4  • 

49 

8    to  8  * 

61 

2x  2  x2  f 

16 

8*  to  6 

62 

6x  6  x6  * 

115 

6*  to  6 

46 

Fittings 

on  the  above  Miscellaneous  List  may  vary 

in  weight  15  per  cent.     All  combinations  of  Converse 

and    threaded   pipe,  and   Converse  and    cast-iron   pipe 

connections 

will  be  uncertain  weights,  as  patterns  are 

changed  for  each  requirement. 

NATIONAL  TUBE  COMPANY. 


SPECIAL 

Steel  Lap- Welded  Pipe 

FITTED  WITH 

MATHESON  PATENT  JOINT. 


0.  D. 

Thick- 
ness 
Nearest 
B.  W.  G. 

Approximate  Weights. 

Lead 
Space. 

Size  of 
Rings. 

Per  Foot 
Complete. 

Pounds  of 
Lead 
in  Joint. 

2 

13 

1.91 

# 

X 

A*# 

3 

12 

3.40 

1 

% 

A*tf 

4 

io# 

5.25 

1^ 

A 

X*^ 

5 

9^ 

7.30 

2 

A 

X*x 

6 

9^ 

8.75 

3^ 

T3ir 

Ail 

7 

9 

10.75 

4 

A 

A^i 

8 

8K 

13.00 

5 

A 

^xl 

9 

8^ 

14.65 

6X 

-^ 

#*1 

10 

8 

17.08 

7/8 

A 

T7^l 

12 

6 

25.12 

11^ 

^ 

KxlX 

14 

5K    - 

31.00 

13^ 

X 

^xiy 

15 

4K 

35.42 

15 

X 

^xlX 

16 

3K 

42.00 

16 

X 

>^xlX 

18 

1* 

56.00 

26^ 

N 

^xlX 

20 

0^ 

67.00 

30 

H 

^xlX 

—  —  .     |j^ 

34                         NATIONAL  TUBE  COMPANY. 

WEIGHT    OF    FITTINGS. 

Matheson  Joint, 

Heavy-faced    figures   indicate   openings    tapped    for 

Standard  Pipe. 

TEES. 

SIZE. 

Wgt.   Ibs. 

SIZE.              ^ 

Wgt.   Ibs. 

2  x  2  x 

2 

11 

6x6x4 

96 

3  x  3  x 

3 

19 

6x6x3 

93 

3  x  3  x 

4 

35 

6x4x4 

100 

4  x  4  x 

4 

35 

6x3x6 

90 

4  x  4  x 

4 

39 

7x7x7 

4  x  4  x 

8 

35 

7x7x6 

lis 

4  x  4  x 

3 

35 

8x8x8 

159 

4  x  4  x 

2 

37 

8x8x6 

173 

4  x  4  x 

2 

36 

8x8x4 

172 

4  x  4  x 

1 

34 

8x6x8 

176 

4  x  4  x 

6 

98 

9x9x9 

4  x  3  x 

4 

35 

10  x  10  x  10 

256 

5  x  5   x 

5 

41 

10  x  10  x     8 

270 

5  x  5  x 

4 

58 

10  x  10  x     6 

268 

5  x  5  x 

4 

58 

10  x  10  x     4 

285 

5  x  3  x 

5 

56 

11  x  11  x  11 

353 

6  x  6  x 

6 

91 

12  x  12  x  12 

ELBOWS. 

SIZE. 

Degree.  Wgt  Ibs. 

SIZE. 

Degree 

Wgt.  Ibs. 

2x2 

90               9 

8x8 

30 

60 

3x3 

45           11 

8x8 

45 

77 

3x3 

90           18 

8x8 

90 

137 

4x4 

45           22 

9x9 

45 

4x4 

90           33 

9x9 

90 

4x3 

90           32 

10  x  10 

13 

66 

5x5 

45           36 

10  x  10 

16 

78 

5x5 

90           45 

10  x  10 

18 

79 

6x6 

30           29 

10  x  10 

25 

90 

6x6 

45           45 

10  x  10 

28 

98 

6x6 

45           45 

10  x  10 

30 

98 

6x6 

90           79 

10  x  10 

36 

110 

7x7 

45           57 

10  x  10 

45 

126 

7x7 

90         100 

10  x  10 

90 

235 

n  1 

NATIONAL  TUBE  COMPANY.                       35 

ELBOWS. 

SIZE.           Degree 

Weight. 
Ibs. 

SIZE. 

Degree 

Weight 
'     Ibs. 

11    x   11            45 

160 

12  x    12 

45 

11    x   11            60 

192 

12  x  12 

90 

372 

11   X   11            90 

255 

CROSSES. 

SIZE. 

Weight. 

SIZE. 

Weight. 

Ibs. 

Ibs. 

2x2    x    2  x    2 

13 

6x4    x    3x    3 

125 

3x3    x    3x    3 

28 

7x7    x   7x    7 

135 

4x4    x    4x    4 

42 

7x7    x    6x    6 

153 

4x4    x    4x    3 

43 

8x8    x    8x    8 

200 

4x4    x    3  x    3 

46 

8x8    x    * 

x   4 

229 

4x4    x    2x    2 

45 

8x8   x    8x   6 

230 

4x4    x    2x   2 

43 

8x8   x    4x    4 

209 

4x3    x    3x    3 

45 

8x8   x  14  x  16 

1190 

5x5    x    5  x    5 

66 

8x6    x    8x    6 

220 

5x5    x    5  x    4 

69 

8x6    x    g 

x    4 

235 

5x5    x    4x  4: 

74 

8x6    x    3  x    3 

238 

5x4   x    5  x    5 

72 

8x4    x    4x    4 

218 

6x6    x    6x    6 

108 

9x9    x    9x    9 

6x6    x    4x    4 

117 

10  x  10  x  10  x  10 

337 

6x6    x    4x    3 

120 

10  x  10  x  10  x    8 

339 

6x4    x    4x    4 

127 

12  x  12x12  x  12 

Heavy  faced  figures  indicate  openings  tapped  for 

Standard  Pipe. 

'      36                        NATIONAL  TUBE  COMPANY. 

REDUCERS. 

SIZE. 

Weight 
Lbs. 

SIZE. 

Weight 
Lbs. 

SIZE. 

Weight 
Lbl 

3x2 

6x4 

21 

9x8 

4x3 

11 

6x3 

9x7 

4x3 

14 

6x3 

25 

9x6 

4x2 

12 

7x6 

10  x  9 

5x5 

19 

7x5 

10  x  8 

50 

5x4 

17 

8x7 

10  x  6 

46 

5x3 

8x6 

39 

10  x  4 

52 

6x5 

8x4 

43 

12  xlO 

75 

6x4 

22 

PLUGS. 

SIZE. 

Weight 
Lbs. 

SIZE. 

Weight 
Lbs. 

SIZE. 

Weight 
Lbf. 

2 

1 

6 

7 

10 

23 

3 

2 

7 

13 

12 

4 

3 

8 

15 

14 

58 

5 

5 

9 

16 

88 

Heavy-faced  figures  indicate  openings  tapped   for 
Standard  Pipe. 
Some  of  the  weights  in  these  tables  of  Matheson  Joint 
Fittings  are  not  given  ;  the  reason  being  that  there  are 
not  Standard  patterns  for  sizes  where  weights  are  omitted 
and  the  patterns  of  some  other  size  are  made  adaptable 
for  same.     This  would  cause  a  variation  in  weights,  and 
for  this  reason  it  is  thought  best  to  give  no  fixed  weights 
for  fittings  so  manufactured. 

$n  n? 

NATIONAL  TUBE  COMPANY. 


PLAIN  UPSET. 


UPSET  TUBES  are  becoming  very  generally  used  for 
Marine  Boiler  work  ;  in  many  cases  the  ordinary,  as  well 
as  the  Stay  Tubes,  are  thickened  or  upset  on  ends, 
greater  durability  and  strength  being  claimed  for  same. 

The  difficulties  encountered  in  upsetting  ends  of  tubes 
are  not  generally  appreciated,  and  upsets  are  often  asked 
for  that  are  either  very  difficult  or  practically  impossible 
to  make.  As  a  guide  for  ordering  such  tubes  a  set  of 
tables  has  been  prepared  showing  the  practicable  limits 
that  should  be  observed  in  tubes  of  this  kind.  If  a 
greater  diameter  is  required  for  upset  end  than  that 
shown  on  table  giving  maximum  upset — this  can  be 
accomplished  by  expanding  the  end  after  upsetting  as 
is  shown  in  the  cut  below.  The  tables  are  all  based  on 
an  upset  2^  inches  long  which  is  the  usual  length  for 
Boiler  Stay  Tubes.  If  shorter  length  will  answer  a  heavier 
upset  than  those  shown  on  maximum  table  can  be 
secured. 


UPSET  AND 
SWELLED. 


NATIONAL  TUBE   COMPANY. 


TIONAL  TUBE  COMPANY. 
ING  ORDINARY  UPSET  FOR  TUB 


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NATIONAL  TUBE  COMPANY. 


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NATIONAL  TUBE  COMPANY. 


FFICULT)  FOR  TUB 


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NATIONAL  TUBE  COMPANY. 


PIPE  BENDS. 

The  attached  table  gives  the  advisable  radius  and  the 
greatest  and  least  radii  to  which  standard  thickness 
pipe  may  be  bent. 

If  the  radius  must  be  reduced  from  the  minimum  given 
in  the  table,  the  thickness  of  the  pipe  must  be  increased. 
For  such  bends  it  is  best  to  submit  sketch. 

When  the  radius  is  greater  than  the  maximum  given 
in  the  list,  the  bend  is  apt  to  look  like  a  series  of  kinks, 
owing  to  the  Bender  having  to  take  short  heats,  unless 
the  radius  is  so  great  that  the  pipe  may  be  bent  cold. 

With  offset  bends  try  to  make  according  to  Drawing 
F.-26i,  rather  than  Drawings  F.-257  or  262.  The 
straight  length  between  the  bends  is  of  advantage  to  the 
pipe  Bender. 

With  the  welded  flanges  there  must  be  a  short  straight 
length  of  pipe  adjacent  to  each  flange.  On  sizes  under 
4  inches  this  should  equal,  at  least,  one  and  a  half  diam- 
eters. On  sizes  over  4  inches  it  should  equal,  at  least, 
one  diameter  of  the  pipe.  In  all  cases  it  is  better  if  equal 
to  two  diameters  of  straight  pipe. 

BENT  TUBES. 

These  are  more  difficult  to  bend  than  standard  weight 
pipe.  Try  not  to  vary  from  the  advisable  radius  given  in 
the  table.  With  tubes  it  is  frequently  necessary  to  in- 
crease the  thickness  over  that  of  standard  boiler  tubes  in 
order  to  bend  them. 


42                        NATIONAL  TUBE  COMPANY. 

TABLE  OF  RADH 

FOR 

PIPE    BENDS. 

Pipe  Size. 

Minimum 
Radius. 

Maximum 
Radius. 

Advisable 
Radius. 

Inches. 

Inches. 

Inches. 

Inches. 

2K 

10 

25 

15 

3 

12 

30 

18 

3K 

14 

35 

21 

4 

16 

40 

24 

*K 

18 

45 

27 

5 

20 

50 

30 

6 

24 

60 

36 

7 

28 

70 

42 

8 

32 

80 

48 

9 

36 

90 

54 

10 

40 

100 

60 

11 

44 

110 

66 

12 

48 

120 

72 

14  o.  d. 

60 

140 

84 

15    " 

68* 

145 

90 

16     " 

76 

150 

100 

18     " 

90 

165 

125 

20     " 

120 

180 

150 

22    " 

132 

198 

165 

24     " 

144 

216 

180 

NATIONAL  TUBE  COMPANY.                       43 

STOCK  PIPE  BENDS 

AMERICAN  OR  ENGLISH  STANDARD 

THREADS  AND  COUPLINGS. 

Irt 

*  -A  * 

Pipe  Size. 

Radius 
"R." 

Centre  To 
Face  "A." 

Inches. 

Inches, 
l/^ 

Inches. 
2 

H 

1 

2 

| 

3 

?* 

3 

8 

10 

4 

10^ 

m 

5 

14# 

18^ 

1  :  

NATIONAL  TUBE  COMPANY. 


OFFSET  BEND,  No.  F.  257.  ANGLE  BEND,  No.  F.  260. 


OFFSET  BEND,  No.  F.  261. 


1800  BEND,  No.  F.  258. 


go"  BEND,  No.  F.  259. 


DIMENSIONS 


National  Trolley  Poles 


DEFLECTIONS 
UNDER  STATED  LOADS 


If                      °& 

46                         NATIONAL  TUBE  COMPANY. 

S  Length  of  Pole,  34  feet.  End  of  Pole  6  feet  in  ground. 

TABLE  OF  DEFLECTIONS  MEASURED  AT  FREE  END. 

TOP  LINE  GIVES  LOADS  IN  POUNDS  APPLIED  18"  FROM  END. 

I 

^          TH 
GO*        OS 

CO       OS 

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Length  of  Pole,  33  feet.  End  of  Pole  6  feet  in  ground. 

TABLE  OF  DEFLECTIONS  MEASURED  AT  FREE  END. 

TOP  LINE  GIVES  LOADS  IN  POUNDS  APPLIED  18"  FROM  END. 

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60                       NATIONAL  TUBE  COMPANY. 

3  Length  of  Pole,  32  feet.  End  of  Pole  6  feet  in  ground. 

TABLE  OF  DEFLECTIONS  MEASURED  AT  FREE  END. 

TOP  LINE  GIVES  LOADS  IN  POUNDS  APPLIED  18"  FROM  END. 

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TABLE  OF  DEFLECTIONS  MEASURED  AT  FREE  END. 

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64                      NATIONAL  TUBE  COMPANY. 

Length  of  Pole,  30  feet.  End  of  Pole  6  feet  in  ground. 

TABLE  OF  DEFLECTIONS  MEASURED  AT  FREE  END. 

§     * 

0        O              ||    O 

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58                       NATIONAL  TUBE  COMPANY. 

^  Length  of  Pole,  28  feet.  End  of  Pole  6  feet  in  ground. 

TABLE  OF  DEFLECTIONS  MEASURED  AT  FREE  END. 

TOP  LINE  GIVES  LOADS  IN  POUNDS  APPLIED  18"  FROM  END. 

1 

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CD:  r  »c-  ooicoicoo^  -  o-   - 

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o*  -    :  cow-   c-   -  cow-  o  -   ww- 

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hglsSISS:  :8:S 

>        t>  CD        CO  1C  CD  1C 1C 


°<  CO  W  CO  CO  W  CO  W  -    CO  W  -     CO  W  CO  CO  W 

o'o'o'o'o'oo'o      o'o     o'o'oo'o 


«  -     -O.     .W,.    ^0^    •          i    <?« 

co-   -o:   -co.   -o-   -co-o- 

00  OO  I>  i>  CO        CO 


60                       NATIONAL  TUBE  COMPANY. 

Length  of  Pole,  27  feet.  End  of  Pole  6  feet  in  ground. 

TABI,E  OF  DEFLECTIONS  MEASURED  AT  FREE  END. 

TOP  LINE  GIVES  LOADS  IN  POUNDS  APPLIED  18"  FROM  END. 

| 

3    8       II   8 

1 

CO        CO 

1 

3  s  3 

1 

|3T3 

1 

CO*        CO        CO*        T|* 

1 

CO        CO*        CO        CO        TH        Tp 

1 

00       O       CO        O       Tt<       00 
00        TH        CO        CO        00        TH 

1 

1111^1^3 

o 

g 

[JJJJsfTl 

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THrH-rHCOCOCOCOCOCO 

§ 

"^iOCOOCOOSCOTHOO 

§'  ^ 

W         co 

™x 

COCO-          CO-          COCO"          - 
00                   0*                  O       O 

•Q'O 

§::§-§     g     8     s 

MIDDLE. 

8'-6" 

..O.HX 

1>CO                        COTHCOTHO-rH 

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•a-o 

§=:§:§§§: 

g       ^ 

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NDIHJ. 

iOCOO*>COlOCO»OCO 

o'o'oo'ooo'o'o 

'Q  'O 

§      2      . 

05                                                                               OS 

•«*.aM 

||  |  S.I  I  1  1  i 

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COTHW5COi>OOOSOTH 

ooooooooooooooosos 

NATIONAL  TUBE  COMPANY. 


o 

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^H  I    O?  00  00 CO 


5J>CO«DOOO?OO 
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*  CQ  CO*  CO*  CO  ^  T»  to  10 


5  T-I  g  00  r-J  W  O6  ^ 


acoeoeo^^ioiogo 


S-i-iOOCO^OOOOCOOlCOWWO 
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O  O  O  O  O  O  O  r 


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5OT-HO? 


OOOOOooOOOOOOO 


s  :  §=  : 


1O        CO  10  to  t 


OO        O  00        O        OO 


:  5  §:  : 


O^ODJ>^OO^OO^     Tj^OO        0>0^^-iiO 
Tt<  CO  O5  CO  CO  <?3  CO  Oi  -    CO  <73  -    CO  Ci  CO  CO  C5 

OOOOOOOO        OO        OOOOO 


8:  - 


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to      go 


JOOOOiiO-^t^T^T-iOCO^lO'^Ci 
THCOIOCQIOC^      •  ""  —  "     ^^ — :  -     " 


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62                       NATIONAL  TUBE  COMPANY. 

^  Length  of  Pole,  26  feet.  End  of  Pole  6  feet  in  ground. 

TABLE  OF  DEFLECTIONS  MEASURED  AT  FREE  END. 

TOP  LINE  GIVES  LOADS  IN  POUNDS  APPLIED  18"  FROM  END. 

§ 

CO 
CO 

O        CO              ||    0 

? 

0 

§ 

o 

CO 

§  §  $ 

1 

^  £  s 

1 

§    5    g    S 

CO*        CO*        CO        CO 

1 

ex?      co'      co      co 

* 

CO 

1 

*:   ®.   3    « 

C>        «        CO        CO 

s  s 

CO*        CO 

I 

CD        CO        TH        CO 
rt<        CD        00        0 

CJ        04        <N        CO 

00        0        00        0        00 
C?        CO        OO        <??        i^ 

1 

T-I        O5        CD        IO 
W        CO        1C        i> 

tO        rj<        O5        OO        O 
O5        C5        "*        t-        CO 

OJ        CO        CO        CO        ^ 

I 

^1^111111 

1 

O?        CD        O5        T$< 
t-        00        05        TH 

T-H               T-I              T-I              CJ 

C3        OJ        C?        CX*        CO 

1 

^        §        °«        » 

O5        T-t        CQ        1C        OO 

T-I      o?      oi      cxi      cxj 

1 

^    g    9    S 

"*        0        ^        0        05 

CD        00        05        T-H        CO 

T-I             T-I             T-I             O?             O* 

d      «9 

g  «i 

'3IOIHX 

CXi         T-I                      O 
T-<        OO                    CQ 
CO        C?                    O? 

o     o*             o 

OO        O 

»       o>      <w      -        - 

0       O 

•<3  '0 

0        „          „          (M 

:      8     §     8     c 

MIDDLE. 

8-2" 

•*»«X 

O        0                    0 

W        CO        CJ        CO        O 

o      o      o     o     o 

'a  'o 

s  =    =    s 

OO                                00 

S          0       cf       0        = 
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BUTT. 
14'-4" 

•»3IHi 

o     o     o     o 

0        0        O        0        0 

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05* 

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NATIONAL  TUBE  COMPANY. 


2 

bo 
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END. 


FR 


DE 


O  O  •*  O?  O  C3  TH 

00  TH  1O  00  OJ  »O  00 

ext  eo  eo  co  Tji  TJH  ^' 


t>COCOTt*OO 
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CQ»OO5COt>THC 


OOOOTH-rH-rHTHT-lT 


TH  TH  o*  oa  <?*  ext  eo 


W(MC5CO 


OTHO)T^lOi>O5TH 


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-    OO1OO1OO1O-    -    O- 


CO IQ         CO  It 


00  „     .    -rri  OO  „     W5  ^     ^    TH  »O  „    CO,    OO  CO  >. 

01  •»     -    CO  O?  »    Oi  -     -    CO  O5  -    CNJ  ~    Ct  Ct  ~ 

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Iz  8Ss  §S§§-  =  §=  r 

CO        t>CO*        COlCCo'lO  IQ 


^c^  c8cococ5co  c5  -   cow-   cowcoco^ 
o'oooo'o'oo     o'o     o'oo'o'o 


^ 


64                       NATIONAL  TUBE  COMPANY. 

•f  Length  of  Pole,  25  feet.  End  of  Pole  6  feet  in  ground. 

TABLE  OF  DEFLECTIONS  MEASURED  AT  FREE  END. 

TOP  LINE  GIVES  LOADS  IN  POUNDS  APPLIED  18"  FROM  END. 

1 

CO        OO 
CO        CO 

C§       CO 

| 

JO        OS        *>• 

TH         CO         JO 

1 

co"      co      co 

3 

CO 

1 

CO        ^        OS 
i>       OS        O 

co      co'      co 

CO        C^ 

CO        CO* 

1 

CO        CO       ^H 
JO        *>        00 

CO*        CO*        CO 

CO        OO        OO 

1 

i-HO5COCOOi>C5CO 

CO        CO        CO 

CO        CO        CO        CO        CO 

1 

OCOOOOCOCOCOCD-^i 
THCOCOCOOOOCOJOO 

CO        CO        CO 

CO        CO        CO        CO        CO        ^ 

I 

00         0         TH 

^        ^        JO        CO        O        -^ 
CO        JO        i>        OS        CO        CO 

1-1        CO        CO 

CO         CO        CO        CO        CO        CO 

§ 

&       00       8 

OO        CO        JO        TH        JO        CO 
O        CO        "*        CO        00        CO 

TH-rHTHCococo'cococo 

1 

•H/l         JO        CO 

CO         t>        ^        00        OS         CO 
00        OS        TH        CO        "tf        OO 

TH        TH        CO        CO        CO*        CO 

I 

$    S    5 

CO        OS        "*         JO        -^        CO 

JO         CO         OO         OS         TH         ^ 

| 

JO        CO        00 

O             TH             TH 

O        TH        CO        CO        00        CO 
CO        ^        JO        CO        J>        O 

Q        co 
fc        J 

W         co 

,0,HX 

TH           OO 

CO        CO        " 
0       0 

O                   OO        O 
O                    00 

•a  -o 

8     :      = 

i> 

^                    0        CO        0 

CO        -          O        CO        0 

MIDDLE. 

7'-10" 

•30.HX 

t-        CO 

CO        O 

O       0 

TH          S          TH-          00          8          SO 

CO        CO        CO        CO        CO        CO 

o*      o      o      o      o      o 

a*o 

8    -     - 

00 

§O        CO        O 
;       o      co      o      - 

00                 .  OO        OO        00 

«                    T3 

.O.HX 

JO        CO        O 
CO        CO        O 
CO        JO        JO 

t-        CO        JO        CO        JO        CO 

CO          O          t—          TH          i>          TH 

^        ^        CO        CO        CO        CO 

o     o     o 

o     o     o     o     o     o 

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§ 

-     -     -     -     §    - 

OS* 

OS* 

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COTHOOSOOOOi>J>*CO 

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NATIONAL  TUBE  COMPANY. 


p 

I 

H 
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w 

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SO  -rH  •*& 


tO  T_|  T^H  ,-( 

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!  CO  CO  CO 


CDCOTt<COOCOO3O 
CO  CO  O  03  CO  00  T-I  CD 

03*  03*  CO  CO  CO  CO  -^  TE__ 


HO3O3O3cocoeoeo^H^ioio 


'd'O 


-I0303030303COCO 


^OOCOCOCOi-IOSOT-iOS'i-l.    . 


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THO3OiO3COCOCOCO^^tOlOCDCO£>OOO5 

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CD  1O  1O  to  ^  1O  ^ 


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3  ,     OCOOCO  „ 
3  ~    O  tO  O  10  - 

ggi        }>  CD        CO  1O  CD  1O 


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00  00  i>  t>  CO         CO* 


66                        NATIONAL  TUBE  COMPANY. 

pj  Length  of  Pole,  24  feet.  End  of  Pole  6  feet  in  ground. 

TABLE  OF  DEFLECTIONS  MEASURED  AT  FREE  END. 

TOP  LINE  GIVES  LOADS  IN  POUNDS  APPLIED  18"  FROM  END. 

i 

1O        CO        OO              II    O 

10        00 
CO        CO 

1 

O       ^f        CO       00 
00        O        CO        -* 

CO        CO        CO        CO 

1 

1O        CO        OO        O        CO 

§ 

1  1  1  I  1 

CO        CO        CO        CO        CO 

CO 
CO 

1 

CO        CO        CO        CO        CO 

CO        CO        CO 

1 

OS        0        CO        ^        CD 
TH        CO        CO        CO        CO 

00        O        CO        i> 
CO        CO*        CO        CO 

CO 

10        0        ^*        00        0 
i>        OS        O        TH        CO 

OO        OO        CO        -rH 
JO        i>        O        -^ 

CO        CO      -CO        CO 

1 

OO        TH        -^        CO        CO 
10        i>        00        OS        TH 

g         §         g         TH- 

THTHi-lTHCOCOCOCOCO 

1 

S    g    8'  S    3 

CO        CO        CO        10 
O       CO       "*       i> 

CO        CO        CO        CO 

IS  2  2  *  2 

TH             1O             TH             TH 
TH            TH            CO            CO 

i 

0        TH        CO        CO        55 

10        CD        00        O 

1 

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TH        00                    CO 
CO        CO        -          CO        » 

00                    O 

CO        CO        -          - 
0        0 

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o      „        „       co 

§co      o 
CO        O        - 

MIDDLE. 

7-6" 

«mx 

t-        CO                     CO        TH 
CO        O                    TH        00 

•<*      •*              co      co 

00                   O    •    O 

TH        00        0        00 
CO        CO        CO        CO 

O        0        0        0 

•a-o 

00                                00 

8    §    8    = 

OO        OO        OO 

E   2 

w 

•HO.HX 

1  §  1  S  1  II  §  !  § 

o      o      o     o      o 

0000 

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CO 

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CD        CD        CO        CD        CD 
CO        CO        CO        CO        CO 

CO        CO        CO        CO 

NATIONAL  TUBE  COMPANY. 


be 

. 


FREE  END. 


TIONS  MEASURED 


DE 


TA 


T-H  I    0303  03  CO 


21 


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co  oi  co  co  w 
o'o'o'o'o'o'o'o      o'o      o'o'o'o'o 


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QO  00 


SEAMLESS 
TUBULAR  GOODS 


NATIONAL  TUBE  COMPANY. 


SEAMLESS  DRAWN  TUBING. 


In  submitting  the  following  information  on  the  subject 
of  Seamless  Tubing,  together  with  the  accompanying 
tables,  etc.,  we  call  attention  to  the  rapid  strides  made  in 
the  demand  and  in  process  of  manufacture  of  this  grade 
of  Tubes  in  the  last  few  years.  These  Tubes  are  becom- 
ing generally  used  for  high  grade  Boiler  work,  where 
high  steam  pressures  are  required ,  especially  for  Marine 
Boilers,  the  Navy  Department  of  all  first-class  Naval 
powers  having  extensively  adopted  the  same.  In  both 
I/ocomotive  and  Stationary  Boilers  the  use  of  this  Tubing 
is  becoming  recognized  as  a  high  grade  quality.  The 
extending  use  of  compressed  air  and  other  gases  under 
high  pressures  has  developed  a  good  demand  for  these 
tubes  for  storage  tanks,  high  pressure  bottles,  transmis- 
sion lines,  etc.  The  absence  of  all  laps  or  seams,  together 
with  uniformity  of  size,  gauge  and  quality,  recommends 
this  grade  of  material  as  very  superior  where  unquestion- 
ed uniformity  and  strength  are  required,  in  connection 
with  the  lightest  weight  available  for  the  purpose. 

Seamless  Tubes  with  varying  thicknesses  of  walls  are 
also  being  used  quite  extensively  for  Mechanical  and 
Engineering  purposes ;  for  bushings,  collars,  hollow 
shafts,  spindles,  axles,  etc.,  in  the  construction  of 
different  classes  of  machinery. 

Different  grades  of  steel  can  be  used,  giving  a  wide 
range  of  ductility  and  tensile  strength,  which  allows  a 
selection  of  material  suited  and  adaptable  to  the  require- 
ments demanded.  The  method  of  manufacture  of  Seam- 
less Tubes  is  such  that  the  possibilities  of  physical  de- 
fects in  material  are  reduced  to  a  minimum. 


NATIONAL  TUBE  COMPANY. 


Extract  from  Proceedings  of  Niagara  Falls  Society  of 

American  Mechanical  Engineers. 

December,  1808. 

What  Constitutes  a  Seamless  Tube? 

41  Henry  Souther  said,  in  the  discussion  of  this  question, 
that  the  scientific  and  technical  designation  of  a  tube, 
'  whether  seamed  or  seamless,  depended  solely  upon  the 
tube  itself,  and  not  upon  the  process  followed  in  its 
manufacture.  Referring  to  the  dictionary  you  will  find 
that  the  word  "seamless"  means  without  seam,  which 
conveys  no  light  upon  the  subject.  Turning  to  the  word 
"seam"  it  is  found  that  it  is  defined  as  a  joint,  suture, 
or  line  of  union,  and  here  in  the  last  term  we  find  the 
key.  A  tube  jointed  in  any  way  cannot  be  seamless.  If, 
in  the  primary  stages  of  its  manufacture,  it  be  lap,  butt 
or  lock- jointed,  it  cannot  by  any  subsequent  operation 
be  deprived  of  the  seam,  and  therefore  cannot  be  con- 
sidered, when  completed,  as  being  seamless  A  strictly 
seamless  tube  may  be  made  by  any  one  of  three  opera- 
tions. First,  a  billet  may  be,  by  successive  steps, 
punched  into  the  form  of  a  tube  with  extremely  thick 
sides  ;  and  these  may  then,  by  the  ordinary  drawing  pro- 
cesses, be  reduced  to  a  tube  with  thin  walls.  Next,  the 
billet  may  be  bored,  or  the  blank  may  be  cast  with  a  hole 
in  it,  and  in  either  case  then  drawn  to  the  required  di- 
mensions. Thirdly,  the  tube  may  be  made  by  the  cup- 
ping process,  which  consists  in  taking  a  disk  of  the 
metal,  forming  it  into  a  cup  shape,  gradually  elongating 
the  cup  and  reducing  it  in  diameter,  and  finally  by  this 
means  producing  a  tube.  Each  and  all  of  these  processes 
yield  a  tube  which  is  absolutely  seamless  and  about 
which  there  is  and  can  be  no  dispute.  In  all  tubes  formed 
with  a  seam  the  edges  have  first  been  separated,  then 
united,  either  by  lap  or  butt  weld,  or  by  some  lock-joint 
system,  and  in  these  the  joint  cannot  be  eliminated  by  any 
after  processes.  The  Custom  House  of  the  United  States 
recognizes  the  difference  between  a  seam  and  a  seamless 
tube.  A  seamless  tube  is  one  in  which  the  walls  have 
never  been  separated  from  the  time  the  metal  was  in  a 
molten  condition  to  the  time  of  the  completion  of  the 
tube." 


NATIONAL  TUBE  COMPANY. 


COLD  DRAWN  TUBES. 

The  Weight  Sheet  for  Seamless  Cold  Drawn  Tubes,  as 
given  on  following  page,  is  applicable  for  Tubes  intended 
for  many  different  purposes.  The  sizes  from  ^  inch  to 
\y2  inch  diameter  and  from  16  to  23  gauge  inclusive  are 
generally  classified  as  Bicycle  Tubing,  on  account  of 
their  very  general  use  in  Bicycle  construction.  They  are 
used,  however,  for  many  other  different  purposes.  These 
Tubes  are  manufactured  from  Open  Hearth  Steel  of 
analysis  best  suited  for  the  purpose.  They  have  a  fine 
finish  and  are  drawn  accurate  to  size  and  gauge.  These 
tubes  are  admirably  adapted  for  all  construction  requir- 
ing a  maximum  strength  and  minimum  weight.  They 
have  great  rigidity  and  are  suited  for  high  transverse 
strains. 

Tubes  for  boiler  purposes,  from  i  inch  to  4  inches,  and 
and  from  13  to  6  gauge  inclusive,  are  made  of  mild  Open 
Hearth  Steel,  of  analysis  best  suited  to  give  toughness 
and  ductility.  The  process  of  manufacture  is  such  that 
only  material  free  from  laps,  seams,  cracks  and  all 
physical  imperfections  can  be  used.  This  insures  a  high 
uniformity  of  quality  and  reduces  the  possibility  of  acci- 
dent, due  to  imperfections  of  material,  laps  and  welds,  to 
a  minimum. 

Tubes  of  thicknesses  other  than  those  given  above  are 
generally  termed  "  Mechanical  Tubes, "  and  are  used  in 
the  construction  of  many  classes  of  machinery  for  bush- 
ings, hollow  shafts  and  spindles,  axles,  collars,  rings, 
ferrules,  pump  barrels,  etc.,  etc.  Often  a  considerable 
saving  in  machine  work  is  effected  by  the  use  of  these 
tubes  in  place  of  parts  heretofore  made  by  boring  and 
turning  round  bars,  the  tubes  admitting  of  a  lighter  and 
stronger  construction  than  by  using  the  former  material. 


NATIONAL  TUBE  COMPANY. 


1 
1 


OH 

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csaooo-^ojcoi-iosocsfNioa 

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llllllil 


74                        NATIONAL  TUBE  COMPANY. 

Table  showing  Weight  per  Foot  in  Pounds  of  Various 

Diameters  and  Thicknesses  of 

HOT  FINISHED  TUBES. 

:§| 

THICKNESS  OF  WALL. 

|| 

M 

* 

H 

A 

M 

A 

M 

H 

H 

1 

2 

4.60 

5.54 

6.40 

7.18 

7.88 

ix 

4.93 

5.96 

6.90 

7.76 

8.54 

M 

5.26 

6.37 

7.40 

8.34 

9.20 

32 

5.59 

6.78 

7.89 

8.92 

9.86 

LX 

5.92 

7.19 

8.38 

9.49 

10.52 

% 

6.25 

7.61 

8.88 

10.07 

11.18 

3X 

6.58 

8.02 

9.38 

10.65 

11.84 

H 

6.91 

8.43 

9.87 

11.23 

12.50 

3 

7.24 

8.84 

10.36 

11.80 

13.16 

14.43 

15.62 

7.57 

9.26 

10.86 

12.38 

13.82 

15.18 

16.45 

ixf 

7.90 

9.67 

11.36 

12.96 

14.48 

15.92 

17.28 

% 

8.23 

10.08 

11.85 

13.54 

15.14 

16.66 

18.10 

ix 

8.56 

10.49 

12  36 

14.11 

15.80 

17.40 

18.92 

KX 

8.89 

10.91 

12.84 

14.69 

16.46 

18.15 

19.75 

% 

9.22 

11.32 

13.34 

15.27 

17.12 

18.89 

20.58 

% 

9.55 

11.73 

13.83 

15.85 

17.78 

19.63 

21.40 

4 

9.88 

12.14 

14.32 

16.42 

18.44 

20.37 

22.22 

25.68 

28.80 

10.21 

12.56 

14.82 

17.00 

19.10 

21.12 

23.05 

26.67 

29.96 

M 

10.54 

12.97 

15.32 

17.58 

19.76 

21.86 

23.88 

27.66 

31.12 

32 

10.87 

13.38 

15.81 

18.16 

20.42 

22.60 

24.70 

28.65 

32.27 

12 

11.20 

13.79 

16.30 

18.73 

21.08 

23.34 

25.52 

29.64 

33.42 

% 

11.53 

14.21 

16.80 

19.31 

21.74 

24.09 

26.35 

30.63 

34.58 

ax 

11.86 

14.62 

17.30 

19.89 

22.40 

24.83 

27.18 

31.62 

35.74 

% 

12.19 

15.03 

17.79 

20.47 

23.06 

25.57 

28.00 

32.61 

36.89 

5 

12.52 

15.44 

18.28 

21.04 

23.74 

26.31 

2S.82 

33.60 

38.04 

42.16 

12.85 

15.86 

18.78 

21.62 

24.40 

27.06 

29.65 

34.59 

39.20 

43.48 

y. 

13.18 

16.27 

19.28 

22.20 

25.06 

27.80 

30.48 

35.58 

40.36 

44.80 

32 

13.51 

16.68 

19.77 

22.78 

25.72 

28.54 

31.30 

36.57 

41  51 

46.12 

i£ 

13.85 

17.10 

20.  «7 

23.36 

26.39 

29.29 

32.13 

37.57 

42.67 

47.45 

% 

14.18 

17.52 

20.77 

23.94 

27.05 

30.04 

32.96 

38.56 

43.83 

48.77 

ax 

14.51 

17.93 

21.27 

24.52 

27.71 

30.78 

33.79 

39.55 

44.99 

50.09 

il 

14.85 

18.35 

21.77 

25.11 

28.38 

31.53 

34.62 

40.55 

46.15 

51.42 

6 

15.18 

18.77 

22.27 

25.69 

29.05 

32.28 

35.45 

41.55 

47.31 

52.75 

15.51 

19.18 

22.77 

26.27 

29.71 

33.03 

36.28 

42.54 

48.47 

54.07 

1? 

15.84 

19.59 

23.26 

26.85 

30.37 

33.77 

37.11 

43.53 

49.  «3 

55.39 

3| 

16.17 

20.01 

23.76 

27.43 

81  04 

34.52 

37.94 

44.53 

.50.79 

56.72 

1^ 

16.50 

20.42 

24.26 

28.01 

31.70 

35.27 

38.77 

45.53 

51.95 

58.05 

sx 

16.83 

20.83 

24.75 

28.59 

32-36 

36.01 

39.60 

46.52 

53.11 

59.37 

ax 

17.17 

21.25 

25.25 

29.17 

33.01 

36.76 

40.43 

47.52 

54.28 

60.70 

K 

17.60 

21.67 

25.75 

29.75 

33.67 

37.51 

41.26 

48.52 

55.44 

62.03 

NATIONAL  TUBE  COMPANY.                        75 

Table  showing  Weight  per  Foot  in  Pounds  of  Various 

Diameters  and  Thicknesses  of 

HOT  FINISHED  TUBES. 

(CONTINUED.) 

-Ss 

THICKNESS  OF  WALL. 

11 

°5 

14 

i5s 

% 

T7* 

w 

A 

% 

% 

% 

1 

7 

17.83 

22.08 

26.25 

30.33 

34.33 

38.25 

42.09 

49.51 

66.60 

63.36 

& 

18.17 

22.50 

26.75 

30.92 

35.00 

38  99 

42.92 

50.51 

57.79 

64.69 

18.50 

22.92 

27.25 

31.49 

35.67 

39.74 

43.75 

51.51 

58.95 

66.02 

% 

18.83 

23.33 

27.75 

32.07 

36.33 

40.49 

44.58 

52.50 

60.11 

67.35 

L^ 

19.16 

23.74 

28.24 

32.66 

36.99 

41.23 

45.41 

53.49 

61.27 

68.67 

% 

19.49 

24.16 

28.74 

33.24 

37.66 

41.98 

46.24 

54.49 

62.43 

70.00 

ax 

19.82 

24.57 

29.24 

33.82 

38.32 

42.73 

47.07 

55.49 

63.57 

71.33 

% 

20.15 

24.98 

29.73 

34.40 

38.98 

43.47 

47.90 

56.48 

64.73 

72.65 

8 

20.48 

25.39 

30.22 

34.97 

39.64 

44.21 

48.72 

57.47 

65.89 

73.97 

% 

20.80 

25.80 

30.71 

35.54 

40.29 

44.95 

49.54 

58.46 

67.04 

75.29 

21.12 

26.20 

31.20 

36.11 

40.94 

45.68 

50.36 

59.44 

68.19 

76.61 

% 

21.44 

26.61 

31.68 

36.68 

41.59 

46.41 

51.17 

60.42 

69.34 

77.92 

U 

21.77 

27.02 

32.17 

37.25 

42.25 

47.15 

51.99 

61.41 

70.49 

79.24 

22.10 

27.44 

32.66 

37.82 

42.90 

47.89 

52.81 

62.39 

71.64 

80  56 

M 

22.43 

27.85 

33.15 

88.39 

43.55 

48.62 

53.63 

63.37 

72.79 

81.87 

9 

22.76 

28.26 

33.64 

38.96 

44.20 

49.36 

54.44 

64.35 

73.93 

83.18 

9 

23.08 

28.67 

34.13 

39.53 

44.85 

50.09 

55.25 

65.33 

75.07 

84.49 

i^ 

23.41 

29.08 

34.63 

40.11 

45.51 

50.83 

fi6.07 

66.31 

76  22 

85.80 

N 

23.74 

29.48 

35.12 

40.69 

46.17 

51.57 

56.89 

67.29 

77.37 

87.11 

s2 

24.07 

29.88 

35.61 

41.26 

46.83 

52.31 

57.71 

68.27 

78.51 

88.42 

H 

24.40 

30.29 

36.10 

41.83 

47.48 

53.05 

5S.53 

69.25 

79.65 

89.73 

g 

24-73 

30.71 

36.60 

42.41 

48.14 

53.79 

59.36 

70.24 

80.80 

91.04 

9 

25.06 

31.12 

37.10 

42.99 

48.80 

54.53 

60.18 

71.23 

81.95 

92.35 

9 

25.39 

31  53 

37.59 

43.57 

49.46 

55.27 

61.00 

72.22 

83.10 

93.66 

10 

25.72 

31.94 

38.08 

44.14 

50.12 

56.01 

61.82 

73.20 

84.25 

94.97 

% 

26.04 

32.35 

38.57 

44.71 

50.77 

56.75 

62.64 

74.18 

85.40 

96.28 

p 

26.36 

32.75 

39.06 

45.28 

51.42 

57.48 

63.46 

75.16 

86.54 

97.59 

26.68 

33.15 

39.54 

45.85 

52  07 

58.21 

64.27 

76.14 

87.68 

98  90 

1^ 

27.01 

33.56 

40.03 

46.42 

52.73 

58.95 

65.09 

77.13 

88.83 

100.21 

•I 

27.34 

33.97 

40.52 

46.99 

53.37 

59.69 

65.91 

78.11 

89.98 

101.52 

y 

27.67 

34.38 

41.01 

47.56 

54.02 

60.42 

66.73 

79.09 

91.13 

102.83 

8 

28.00 

34.79 

41.50 

48.13 

54.68 

61.15 

67.54 

80.07 

92.27 

104.14 

11 

28.32 

35.20 

41.99 

48.70 

55.33 

61.88 

68.35 

81.05 

93.41 

105.45 

1^ 

28.65 

35.61 

42.49 

49.28 

55.99 

62.62 

69.17 

82  03 

94.56 

106.76 

N 

28.98 

3R.02 

42.98 

49.8? 

56.65 

63.36 

69.99 

83.01 

95.71 

108.07 

G 

29.31 

36.43 

43.47 

50.44 

57.31 

64.10 

70.81 

83.99 

96.85 

109.38 

L< 

29.64 

36.84 

43.96 

51.01 

57.96 

64.84 

71.63 

84.97|  97.99 

110.69 

p 

29.97 

37.26 

44.46 

51.59 

58.60 

65.58 

72.46 

85.961  99.14 

112.00 

iS 

30.30 

37.67 

44.96 

52.17 

59.26 

66.32 

73.28 

86.95 

100.29 

113.31 

| 

30.63 

38.08 

45.45 

52.74 

59.92 

67.06 

74.10 

87.94 

101.44 

114.62 

76                NATIONAL  TUBE  COMPANY. 

Table  showing  Weight  per  Foot  in  Pounds  of  Various 

Diameters  and  Thicknesses  of 

HOT  FINISHED  TUBES. 

(CONTINUED.) 

•S| 

THICKNESS  OF  WALL. 

y 

X 

A 

« 

ft 

H 

* 

* 

H 

* 

1 

12 

30.96 

38.49 

45.94 

53.31 

60.58 

67.80 

74.92 

88.92 

102.59 

115.93 

31.28 

38.90 

46.43 

53.88 

61.23 

68.54 

75.74 

89.90 

103.73117.24 

/4 

31.60 

39.30 

46.92 

54.45 

61.88 

69.27 

76.56 

90.88 

104.87118.55 

ax 

31.92 

39.70 

47.40 

55.02 

62.53 

70.00 

77.37 

91.86 

106.01 

119.86 

IX 

32.25 

40.11 

47.89 

55.59 

63.19 

70.74 

78.19 

92.85 

107.16 

121.17 

% 

32.58 

40.52 

48  38 

56  16 

63.84 

71.48 

79.01 

93.83 

108.31  122.48 

a^ 

32.92 

40.94 

48.88 

56.74 

64.50 

72.22 

79.84 

94.82 

109.47,123.80 

% 

33.26 

41.36 

49.38 

57.32 

65.16 

72.96 

80.66 

95.81 

110.62125.12 

13 

33.60 

41.79 

49.89 

57.91 

65.83 

73.71 

81.49 

96.81 

111.78126.45 

ix 

33.94 

42.21 

50.40 

58.50 

66.50 

74.46 

82.32 

97.80 

112.94 

127.77 

IX 

34.28 

42.64 

50.91 

59.10 

67.18 

75.22 

83.16    98.80 

114.11 

129.10 

% 

34.62 

43.06 

51.42 

59.69 

67.86 

75.98 

84.00 

99.80 

115.28130.43 

IX 

34.96 

43.49 

51.93 

60.29 

68.54 

76.75 

84.85 

100.81 

116.45  131.77 

% 

35.28 

43.89 

52.42 

60.86 

69.20 

77.49 

85.68ll01.80 

117.60133.08 

ft£ 

35.59 

44.29 

52.90 

61.43 

69.85 

78.28 

86.50,102.79 

118.75 

134.39 

% 

35.90 

44.68 

53.38 

61.99 

70.50 

78.96 

87.32103.78 

119.90 

135.70 

14 

36.20 

45.07 

53.85 

62.55 

71.14 

79.69 

88.13104.76 

121.05 

137.01 

36.52 

45.45 

54.32 

63.10 

71.78 

80.41 

88.94 

105.74 

122.20 

138.32 

IX 

36.85 

45.86 

54.79 

63.66 

72.42 

81.14 

89.75 

106.72 

123.35 

139.64 

sx 

37.19 

46.28 

55.29 

64.22 

73.07 

81.87 

90.57 

107.71 

124.51 

140.97 

/^ 

37.54 

46.71 

55.80 

64.81 

73.72 

82.61 

91.39108.70 

125.67 

142.30 

fix 

37.90 

47.15 

56.32 

65.41 

74.40 

83.35 

92.22'109.70 

126.84 

143.64 

ax 

38.25 

47.59 

56.84 

66.01 

75.08 

84.11 

93.  04)110.69 

128.00 

144.97 

fl 

38.60 

48.03 

57.37 

66.62 

75.77 

84.88 

93.89 

111.69 

129.17 

146.31 

15 

38.94 

48.46 

57.89 

67.23 

76.46 

85.65 

94.74 

112.68 

130.33 

147.64 

ix 

39  27 

48.88 

58.40 

67.83 

77.15 

86.42 

95.59 

113.69 

131.49 

148.97 

IX 

39.60 

49.29 

58.90 

68.42 

77.83 

87.19 

96.44 

114.70 

132.64 

150.29 

a| 

39.92 

49.70 

59.39 

69.00 

78.50 

87.95 

97.29 

115.71 

133.81 

151.61 

ix. 

40.24 

50.10 

59.88 

69.57 

79.16 

88.70 

98.13 

116.72 

134.98 

152.92 

RX 

40.56 

50.50 

60.36 

70.14 

79.81 

89.44 

98.96 

117.73 

136.15154.25        | 

M 

40.88 

50.90 

60.84 

70.70 

80.46 

90  17 

99.78 

118.73 

137.32 

155.58 

fl 

41.20 

51.30 

61.32 

71.26 

81.12 

90.90 

100.59 

119.72 

138.49 

156.91 

16 

41.52 

51.70 

61.80 

71.82 

81.76 

91.62 

101.40 

120.70 

139.65 

158.24 

ix 

41.84 

52.10 

62.28 

72.38 

82.40 

92.34 

102.20J121.67 

140.80 

159.57 

M 

42.14 

52.48 

62.74 

72.92 

83.02 

93.04 

102.98  122.62 

141.92 

160.87 

% 

42.45 

52.87 

63.21 

73.47 

83.65 

93.75 

103.77 

L28.57 

143.04 

162.17 

IX 

42  76 

53.26 

63.68 

74.02 

84.28 

94.45 

104.56 

124.52 

144.16 

163.46 

sx 

43.13 

53.71 

64.21 

74.63 

84.97 

95.23 

105.41 

125.53 

145.33 

164.80 

M 

43.47 

54.11 

64.69 

75.19 

85.61 

95.95 

106.21 

126.49 

146.45 

166.09 

% 

43.82 

54.55 

65.19 

75.77 

86.27 

96.  69 

107.03 

127.47 

147.59 

167.39 

17 

44.19 

55.00 

65.73 

76.37 

86.95 

97.45 

107.87 

128.47 

148.75 

168.71 

NATIONAL  TUBE  COMPANY. 


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Weight  Per  Foot  in  Lbs,  of  Various  Di 

COLD-DRAWN  TUBES. 

(CONTINUED.) 


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NATIONAL  TUBE  COMPANY. 


ges  of 


Weight  Per  Foot  in  Lbs.  of  Vario 

COLD-DRAWN  TU 


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82                        NATIONAL  TUBE  COMPANY. 

TABLE  OF  LENGTHS  AND  WEIGHTS 

OF 

WORKING  BARRELS. 

f—                                  /Working  Barrel              ^^j  '      A 

i  m    >|  1 

iTT5            P« 
Itli  L  J  b  i  r 

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JJ  W  ^^^                     ffe  j 

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T  1    perl"          *         irT      1             U  K  T  f 

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J  J  W         J 

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1  *T  T         L1F7  1  I 

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Length        2  Inch  Barrel 
in  Feet.       Weight  in  Ibs. 

2J/2  Inch  Barrel         3  Inch  Barrel 
Weight  in  Ibs.         Weight  in  Ibs. 

5              32    to   37 
6              35     "    40 
7             38    "    43 
8             41     "    46 
9             44    "    49 

37    to   43            47    to   55 
43     "    49            54    "    62 
49    "    55            61     "    69 
55     "    61             68     "    76 
61     "    67            75     "    83 

• 

NATIONAL  TUBE  COMPANY. 


ILLUSTRATIONS 


Standard  and  Special  Seamless  Cylinders. 


[5  inch  Standard  Seamless  Cylinder. 

(See  Table,  page  84.) 


8  inch  Standard  Seamless  Cylinder. 

(See  Table,  page  85.) 


TENSILE  STRENGTH  or  MATERIAL '=  90.000  LBS. 


8  inch  Special  Seamless  Cylinder. 

(See  Table,  page  86.) 


84                        NATIONAL  TUBE  COMPANY. 

Table  of  Weights  and  Capacities  of  5  inch  Standard 

Seamless  Cylinders. 

Outside  Diameter,  5^B  inches.      Thickness  of  Wall,  ££  inch. 

(See  illustration,  page  83.) 

Tested  to  3700  Ibs.  per  square  inch  Hydrostatic  Pressure. 

Length 
over  all 
in  inches. 

Average 
Weight 
in  IDS. 

Capacity  in 
Cubic  inches. 

Capacity  in 
Cubic  feet. 

Capacity 
Gallons. 

Capacity  in 
Ibs.  Liquid 
Carbonic 
Acid  Gas. 

36 

39.00 

653 

0.3779 

2.83 

15. 

39.47 

663 

0.3839 

2.87 

15.2 

37 

39.94 

673 

0.3900 

2.92 

15.4 

37^3 

40.41 

683 

0.3961 

2.96 

15.6 

38 

40.88 

694 

0.4022 

3.01 

15.8 

38)4 

41.35 

704 

0.4083 

3.05 

16. 

39 

41.82 

714 

0.4143 

3.10 

16.2 

39^2 

42.29 

725 

0.4204 

3.14 

16.4 

40 

42.76 

735 

0.4265 

3.19 

16.6 

40^ 

43.23 

745 

0.4326 

3.23 

16.8 

41 

43.71 

756 

0.4387 

3.28 

17. 

44.18 

766 

0.4447 

3.32 

17.2 

42 

44.65 

776 

0.4508 

3.37 

17.4 

42^ 

45.12 

786 

0.4569 

3.41 

17.6 

43 

45.59 

797 

0.4630 

3.46 

17.8 

46.06 

807 

0.4691 

3.50 

18. 

44 

46.53 

817 

0.4751 

3.55 

18.2 

44^ 

47.00 

828 

0.4812 

3.59 

18.4 

45 

47.47 

838 

0.4873 

3.64 

18.6 

45^ 

47.94 

848 

0.4934 

3.68 

18.8 

46 

48.42 

859 

0.4995 

3.73 

19. 

46^ 

48.89 

869 

0.5055 

3.77 

19.2 

47 

49.36 

879 

0.5116 

3.81 

19.4 

47^ 

49.83 

889 

0.5177 

3.85 

19.6 

48 

50.30 

900 

0.5238 

3.90 

19.8 

48U 

50.77 

910 

0.5299 

3.94 

20. 

49 

51.24 

920 

0.5359 

3.99 

20.2 

49^ 

51.71 

931 

0.5420 

4.03 

20.4 

50     . 

52.18 

941 

0.5481 

4.08 

20.6 

50U 

52.65 

951 

0.5542 

4.12 

20.8 

51 

53.13 

962 

0.5603 

4.17 

21. 

53.60 

972 

0.5663 

4.21 

21.2 

52 

54.07 

982 

0.5724 

4.26 

21.4 

54.54 

992 

0.5785 

4.30 

21.6 

53 

55.01 

1003 

0.5846 

4.35 

21.8 

53^ 

55.48 

1013 

0.5907 

4.39 

22. 

54 

55.95 

1023 

0.5967 

4.44 

22.2 

54^ 

56.42 

1034 

0.6028 

4.48 

22.4 

55 

56.89 

1044 

0.6089 

4.53 

22.6 

57.36 

1054 

0.6150 

4.57 

22.8 

56 

57.84 

1065 

0.6211 

4.62 

23. 

56^ 

58.31 

1075 

0.6271 

4.66 

23.2 

58.78 

1085 

0.6832 

4.71 

23.4 

57^ 

59.25 

1095 

0.6393 

4  75 

23.6 

58 

59.72 

1106 

0.6454 

4.80 

23.8 

58^ 

60.19 

1116 

0.6515 

4.84 

24. 

59 

60.66 

1126 

0.6575 

4.89 

24.2 

59^ 

61.13 

1137 

0.6636 

4.93 

24.4 

60 

61.60 

1147 

0.6697 

4.97 

24.6 

NATIONAL  TUBE  COMPANY.                       85 

Table  of  Weights  and  Capacities  of  8  inch  Standard 

Seamless  Cylinders* 

Outside  Diameter,  8T9a  inches.       Thickness  of  Wall,  &  inch. 

(See  illustration,  page  83.) 

Tested  to  3700  Ibs.  per  square  inch  Hydrostatic  Pressure. 

Length 
over  all 
in  inches. 

Average 
WeigKt 
in  Ibs. 

Capacity  in. 
Cubic  inches. 

Capacity  in 
Cubic  feet. 

%puadsty 

Gallons. 

Capacity  in 
Ibs.  Liquid 
Carbonic 
Acid  Gas. 

36 

69.4 

1781 

1.0307 

7.71 

37. 

36^ 

70.25 

1806 

1.0454 

7.82 

37.5 

37 

71.1 

1832 

.0601 

7.94 

38. 

37^ 

71.95 

1857 

.0783 

8.05 

38.5 

38 

72.8 

1883 

.0895 

8.16 

39. 

38^ 

73.65 

1908 

.1042 

8.27 

39.5 

39 

74.5 

1934 

.1189 

8.38 

40. 

39U 

75.35 

1952 

.1336 

8.49 

40.5 

40 

76.2 

1985 

.1483 

8.60 

41. 

40}^ 

77.05 

2010 

.1630 

8.71 

41.5 

41 

77.9 

2036 

.1778 

8.82 

42. 

41>^ 

78.75 

2061 

.1925 

8.93 

42.5 

42 

79.7 

2087 

.2072 

9.04 

43. 

42^ 

80  55 

2112 

.2219 

9.15 

43.5 

43 

81.4 

2138 

.2368 

9.26 

44. 

43^ 

82.25 

2163 

.2515 

9.37 

44.5 

44 

83.1 

2189 

.2662 

9.48 

45. 

44^ 

83.95 

2214 

.2809 

9.59 

45.5 

45 

84.8 

2240 

2956 

9.70 

46. 

45^ 

85.65 

2265 

.3103 

9.81 

46.5 

'       46 

86.5 

2291 

.3251 

9.92 

47. 

46^ 

87.35 

2316 

.3398 

10.03 

47.5 

47 

88.2 

2342 

.3545 

10.14 

48. 

47^ 

89.05 

2367 

3692 

10.25 

48.5 

48 

89.9 

2393 

.3839 

10.36 

49. 

48J^ 

90.75 

2418 

.3966 

10.47 

49.5 

49 

91.6 

2444 

.4113 

10.58 

50. 

49^ 

92.45 

2469 

.4260 

10.69 

50.5 

50 

93.3 

2495 

.4407 

10.80 

51. 

50^ 

94.1 

2520 

.4554 

10.91 

51.5 

51 

95. 

2546 

.4702 

11.02 

52. 

51H 

95.85 

2571 

.4849 

11.13 

52.5 

52 

96.7 

2597 

.4996 

11.24 

53. 

52\4 

97.55 

2622 

.5143 

11.35 

53.5 

53 

98.4 

2648 

.5290 

11.46 

54. 

53^ 

99.25 

2673 

.5437 

11.57 

54.5 

54 

100.1 

2699 

.5585 

11.68 

55. 

54^3 

100.95 

2724 

.5732 

11.79 

55.5 

55 

101.8 

2750 

.5879 

11.90 

56. 

55^ 

102.65 

2775 

£  .6026 

12.01 

56.5 

56 

103.5 

2801 

.6174 

12.12 

57. 

56^ 

104.35 

2826 

.6321 

12.23 

57.5 

57 

105.2 

2852 

.6468 

12.34 

58. 

57}^ 

106.05 

2877 

.6615 

12.45 

58.5 

58 

106.9 

2903 

.6762 

12.56 

59. 

58J^ 

107.75 

2928 

;   .6909 

12.67 

59.5 

59 

108.6 

2954 

i   .7056 

12.78 

60. 

59J^ 

109.45 

2979 

1.7203 

12.89 

60.5 

60 

110.5 

3005 

1.7303 

13.00 

61. 

,  J 

86                        NATIONAL  TUBE  COMPANY. 

Table  of  Weights  and  Capacities  of  8  inch  Special  Seamless 

Cylinders  for  Holding  Carbonic  Gas. 

Outside  Diameter,  8  inches.       Thickness  of  Wall,  &  inch. 

(See  illustration,  pa£e  83.) 

Tested  to  3000  Ibs.  per  square  inch  Hydrostatic  Pressure. 

Length 
over  all 
in  inches. 

Average 
Weight 
in  IBs. 

Capacity  in 
Cubic  inches. 

Capacity  in 
Cubic  feet. 

<&§*£ 

Gallons. 

Capacity  in 
Ibs.  Liquid 
Carbonic 
Acid  Gas. 

36 

74.2 

1459 

[8443 

~~6731 

30. 

36^ 

75.0 

1482 

.8573 

6.41 

30.4 

37 

75.8 

1504 

.8703 

6.51 

30.9 

37!^ 

76.6 

1526 

.8833 

6.60 

31.3 

38 

77.4 

1549 

.8963 

6.70 

31.8 

38^ 

78.2 

1571 

.9093 

6.80 

32.2 

39 

79.0 

1594 

.9223 

6.89 

32.7 

39^ 

79.8 

1616 

.9353 

6.99 

33.1 

40 

80.6 

1639 

.9483 

7.09 

33.6 

40^ 

81.4 

1661 

.9613 

7.19 

34. 

41 

82.2 

1684 

.9744 

7.28 

34.5 

41^ 

83.0 

1706 

.9874 

7.38 

34.9 

42 

83.8 

1729 

1.0004 

7.48 

35.4 

«W 

84.6 

1751 

1.0134 

7.58 

35.8 

43 

85.4 

1773 

1.0264 

7.68 

36.3 

43^ 

86.2 

1796 

1.0394 

7.77 

36.7 

44 

87.0 

1818 

1.0524 

7.87 

37.2 

44^ 

87.8 

1841 

1.0654 

7.96 

37.6 

45 

8S.6 

1863 

1.0784 

8.06 

38.1 

45^ 

89.4 

1886 

1.0914 

8.16 

38.5 

46 

90.2 

1908 

1.1045 

8.26 

39. 

46J^ 

91.0 

1931 

1.1175 

8.35 

39.4 

47 

91.8 

1953 

1.1305 

8.45 

39.9 

47^ 

92.6 

1976 

1.1435 

8.55 

40.3 

48 

93.4 

1998 

1.1565 

8.65 

40.8 

48^ 

94.2 

2020 

1.1695 

8.74 

41.2 

49 

95.0 

204:1 

1.1825 

8.84 

41.7 

49^ 

95.8 

2067 

1.1955 

8.94 

42.1 

50 

96.6 

2090 

1.2085 

9.04 

42.6 

50^ 

97.4 

2112 

1.2215 

9.13 

43.0 

51 

98.2 

2135 

1.2346 

9.23 

43.5 

51^ 

99.0 

2157 

1.2476 

9.33 

43.9 

52 

99.8 

2180 

1.2606 

9.42 

44.3 

52^ 

100.6 

2202 

1.2736 

9.52 

44.8 

53 

101.4 

2225 

1.2866 

9.62 

45.2 

531^ 

102.2 

2247 

1.2996 

9.72 

45.7 

54 

103.0 

2269 

1.3126 

9.81 

46.1 

54^ 

103.8 

2292 

1  3256 

9.91 

46.6 

55 

104.6 

2314 

1.3386 

10.01 

47.0 

55^ 

105.4 

2337 

1.3516 

10.11 

47.5 

56 

106.2 

2359 

1.3647 

10.20 

47  9 

56^ 

107.0 

2381 

1.3777 

10.30 

48.4 

57 

107.8 

2403 

1.3907 

10.40 

48.8 

57^ 

108.6 

2426 

1.4037 

10.49 

49.3 

58 

109.4 

2449 

1.4167 

10.59 

49.7 

58^ 

110.2 

2471 

1.4297 

10.69 

50  2 

59 

111.0 

2493 

1.4427 

10.79 

50.6 

59^ 

111.8 

2516 

1.4558 

10.88 

51.1 

60 

112.6 

2538 

1.4687 

10.98 

51.5 

• 

NATIONALITUBE  COMPANY. 


Table  of  Weights  and  Capacities  of  Seamless  Cylinders 
of  various  diameters. 


Tested  3700  Ibs.  per  square  inch  Hydrostatic  Pressure. 


14 
15 
16 
17 
19 
20 
21 
22 
24 
25 
27 
28 
30 
33 


43 
46 
50 
53 
56 


66 
70 
74 
79 
85 
90 
94 
98 
103 


6.8 
7.2 
7.8 
8.2 
8.7 
9.2 
9.6 
10. 
10.6 
11. 
11.8 
12. 
12.6 
15. 
16. 
17. 
18. 
20.5 
21.2 
21.7 
22.4 
26. 
26.7 
27.5 
28.1 
32.5 
33. 
34. 
85.2 
39.4 
40.5 


<*H  C-U 

o  o  u 


.5 
.57 
.6 
.67 

.7 
.76 
.78 


.91 
.98 

1. 

1.05 

1.3 
.4 
.43 
.5 
.7 
.8 
.8* 
.88 

2.1 

2.22 

2.3 

2.4 

2.7 

2.8 

2.9 

3. 

3.3 

3.4 


219 
251 


358 
397 
438 
471 
526 
573 
622 
673 
724 
778 
834 
891 
950 
1010 
1072 
1136 
1200 
1267 
1336 
1406 
1477 
1550 
1623 
1699 
1775 
1854 


««1H 

riT3  C3 

*1| 


84.8 
99.5 
115.4 
132.5 
150.7 
169.9 
190.8 
212.6 
235.5 
259.7 
285. 
311.5 


461.7 
495.4 


603. 
641.4 
680.9 
721.5 
763.3 
806.4 
850.5 
895.9 
942.5 
990. 
1039. 


8.29 
9.62 
11.04 
12.56 
14.18 
15.90 
17.72 
19.63 
21.64 
23.75 
25.96 
28.27 
30.68 
33.18 
35.78 
38.48 
41.28 
44.17 
47.17 
50.26 
53.45 
56.74 
60.13 
63.61 
67.20 
70.88 
74.66 
78.54 


88                NATIONAL  TUBE  COMPANY. 

Table  of  Weights  and  Capacities  of  Seamless  Cylinders 

of  various  diameters. 

(CONTINUED.) 

•s 

l|  bb 

VM  C^ 

O  O  bo 

*o  o  bo 

.S«^6i 

oM 

°  o  bo 

E  v 

11 
5 

a 

j> 

}l 

m 

m 

® 

•Si 

li 

11 

11??. 

u 

109 

41.2 

3.47 

1932 

1140.3 

95.03 

i(! 

114 

42.7 

3.62 

2012 

1192.8 

99.40 

IJL| 

|l 

119 

47. 

3.9 

2093 

1245.6 

103.87 

11% 

[2V, 

/'s 

125 

48. 

4. 

2176 

129U.8 

108.43 

12 

:/;-'s 

132 

49. 

4.05 

2261 

1356. 

113.10 

13 

•!'s 

137 

50. 

4.1 

2347 

1414.3 

117.86 

12}/£ 

13,-,. 

13 

143 

55. 

4.5 

2433 

1472.4 

122.72 

12% 

I8fi 

1    ;:j 

150 

56.4 

4.7 

2521 

1532. 

127.68 

13 

''!  - 

162 

57.4 

4.8 

2610 

1592. 

132.73 

|.j  'T 

-1'  0 

168 

58.5 

4.9 

2700 

1664.7 

137.89 

13/4) 

I4:';s 

1?(T 

174 

64.5 

5.4 

2790 

1717.2 

143.14 

13% 

1  4"'s 

7^ 

180 

65.5 

5.5 

2883 

1781.9 

148.49 

14 

1  1  '  S 

7^ 

187 

66.2 

5.55 

2976 

1846.8 

153.94 

l5l/6 

jr 

193 

67.2 

5.6 

3074 

1913.7 

159.48 

wi2 

i  r.  ~ 

J  f; 

200 

74. 

6.1 

3173 

1981.2 

165.13 

14% 

|JJU 

M 

209 

75.6 

6.2 

3265 

2050.4 

170.87 

15 

JglB 

Li 

220 

76.6 

6:3 

3357 

2120.4 

176.71 

IfiJJg 

3| 

227 

77.6 

6.45 

3452 

2191.8 

182.65 

15Vi 

1  r,1'  ., 

V^> 

235 

84.3 

7. 

3548 

2263.2 

188.69 

15% 

10>i 

•y 

244 

85.7 

7.1 

3650 

2337.9 

194  83 

16 

]Z 

255 

87. 

7.2 

3753 

2412. 

201.06 

16^ 

17H 

1/1 

263 

88.7 

7.4 

3855 

2487.6 

207.39 

wB 

17* 

lj_ 

272 

95.5 

8. 

3957 

2565.6 

213.82 

16% 

'l7 

282 

96.7 

8.1 

4058 

2646.6 

220.35 

17 

18ft 

\i 

291 

98.3 

8.2 

4160 

2722.8 

226.98 

1  S'''' 

17 

299 

99.7 

8.3 

4274 

2804.4 

233.71 

WH 

S-V'. 

J9(J 

309 

107. 

8.6 

4389 

2886. 

240.53 

17% 

- 

0 

320 

108.7 

9.06 

4484 

2968.8 

247.45 

18 

!'•''  s 

A 

331 

110.2 

9.2 

4580 

3052.8 

254.47 

1  '>C 

9 

340 

111.5 

9.3 

4686 

3139. 

261.59 

18V6 

IflH 

'  ^i 

350 

119.6 

9.9 

4793 

3225.6 

268.80    ' 

jga/ 

19 

361 

121.3 

10.1 

4900 

3313,4 

276.12 

19 

._•<)].:" 

n 

373 

122.6 

10.2 

5008 

3402. 

283.53 

20  ^'-i 

i'  ii 

382 

126.5 

10.5 

5117 

3492. 

291.04 

191^ 

•](p',' 

5^ 

392 

132.7 

11. 

5226 

3583.2 

298.65 

19% 

21  " 

K2 

403 

134.4 

11.2 

5336 

3676.2 

306.35 

20 

21  M 

% 

415 

136.4 

11.4 

5446 

3769.2 

314.16 

NATIONAL  TUBE  COMPANY. 


Table  of  Weights  and  Capacities  of  5  inch  Standard 

Lap-Welded  Cylinders  (Class  B). 
Outside  Diameter,  5T9B  inches.       Thickness  of  Wall,  Y±  inch. 


Tested  to  3700  Ibs.  per  square  inch  Hydrostatic  Pressure. 


Length 
over  all 
in  inches. 

Average 
Weight 
in  Ibs. 

Capacity  in 
Cubic  inches. 

Capacity  in 
Cubic  feet. 

Capacity 

in  u.  s: 

Gallons. 

Capacity  in 
Ibs.  Liquid 
Carbonic 
Acid  Gas. 

36 

49.14 

618. 

6T3576~ 

2.68 

14. 

49.67 

628. 

0.3636 

2.72 

14.2 

37 

50.20 

638. 

0.3696 

2.77 

14.4 

37^ 

50.73 

648. 

0.3756 

2.81 

14.6 

38 

51.26 

658. 

0.3816 

2.86 

14.8 

51.79 

668. 

0.3876 

2.90 

15. 

39  3 

52.32 

679. 

0.3930 

2.95 

15.2 

39^ 

52.85 

689. 

0.3996 

2.99 

15.4 

40 

53.38 

699. 

0.4056 

3.04 

15.6 

40^ 

53.91 

709. 

0.4116 

3.08 

15.8 

41 

54.44 

719. 

0.4176 

3.13 

16. 

41^6 

54.97 

730. 

0.4236 

3.17 

16.2 

42 

55.50 

740. 

0.4296 

3.22 

16.4 

42^ 

56.03 

750. 

0.4356 

3.26 

16.6 

43 

56.56 

760. 

0.4416 

3.31 

16.8 

43^ 

57.09 

770. 

0.4476 

3.35 

17. 

44 

57.62 

781. 

0.4536 

3.40 

17.2 

44^ 

58.15 

791. 

0.4596 

3.44 

17.4 

45 

58.68 

801. 

0.4656 

3.49 

17.6 

45^ 

59.21 

811. 

0.4716 

3.53 

17.8 

46 

59.74 

821. 

0.4776 

3.58 

18. 

60.27 

831. 

0.4836 

3.62 

18.2 

47 

60.80 

842. 

0  4896 

3.67 

18.4 

47^ 

61.33 

852. 

0.4956 

3.71 

18.6 

48 

61.86 

862. 

0.5016 

3.76 

18.8 

48^ 

62.39 

872. 

0.5076 

3.80 

19. 

49 

62.92 

882. 

0.5136 

3.85 

19.2 

49^ 

63.45 

892. 

0.5196 

3.89 

19.4 

50 

63.98 

903. 

0.5256 

3.94 

19.6 

50V*> 

64.51 

913. 

0.5316 

3.98 

19.8 

51'"" 

65  04 

923. 

0.5376 

4.03 

20. 

51  V^ 

65.57 

933. 

0.5436 

4.07 

20.2 

52 

66.10 

943. 

0.5496 

.12 

20.4 

52^ 

66.63 

954. 

0.5556 

.16 

20.6 

53 

67.16 

964. 

0.5616 

.21 

20.8 

53^ 

67.69 

974. 

C.5676 

.26 

21. 

54 

68.22 

984. 

0.5736 

.31 

21.2 

68.75 

994. 

0.5796 

4.35 

21.4 

55 

69.28 

1005. 

0.5856 

4.40 

21.6 

55^ 

69.81 

1015. 

0.5916 

4.44 

21.8 

56 

70.34 

1025. 

0.5976 

4.48 

22. 

56^ 

70.87 

1035. 

0.6036 

4.52 

22.2 

57 

71.40 

1045. 

0.6096 

4  57 

22.4 

57^ 

71.93 

1055. 

0.6156 

4.61 

22.6 

58 

72.46 

1066. 

0.6216 

4.66 

22.8 

58^ 

72.99 

1076. 

0.6276 

4.70 

23. 

59 

73.52 

1086. 

0.6336 

4.73 

23.2 

59H 

74.05 

1096. 

0.6396 

4.76 

23.4 

60 

74.58 

1106. 

0.6456 

4.80 

23.6 

NATIONAL  TUBE  COMPANY. 


Illustrations  of  Various  Hydraulic  Forgings, 

Various  Styles  of  Valve  Protecting  Caps  used  on  Carbonic 
Acid  Gas  Cylinders. 


These  Caps  are  made  of  light  material  in  various  sizes,  suitable 
for  the  Valves  of  Cylinders. 

Boiler  Shells.  Seamless  Floats 

For  Feed  Water  Regulators. 


These  Shells  are  made  in  var- 
ious sizes  from  6"  Diameter,  by 
i  foot  long,  to  24"  Diameter,  x 
3  feet  long.  They  are  made 
from  Steel  of  55,000  to  60,000 
Tensile  Strength. 


These  Floats  are  made  from  Steel 
of  High  Tensile  Strength,  so  as 
to  make  them  as  light  as  possible. 
They  are  subjected  to  a  Hydros- 
tatic Collapsing  Test  of  sco  Ibs. 
per  square  inch. 


Shrapnel  Forging. 


These  jShrapnels  are  made  of   a'  Special  Grade  of   Steel,    and 
Forged  from  a  Solid  Billet. 


Shrapnel^Forging. 


These  Shrapnels  are  made  of  a 

Special   Grade   of   Steel,  and 

Forged  from  a  Solid  Billet. 


Shrapnel  Forging. 


These  Shrapnels  are  made  of  a 

Special   Grade   of   Steel,  and 

Forged  from  a  Solid  Billet. 


NATIONAL  TUBE  COMPANY. 


Illustrations  of  Various  Hydraulic  Forgings. 

Projectile  Forging. 


Made  from  Special  Grade  of  Steel,  and  Forged  from  a  Solid  Billet. 


Bushing  Forging  for 
Axle  Bearings* 


Separator  Tubular 
Forging. 


These  are  made  from  High 

Grade    Steel,    and    forged 

from  a  Solid  Billet. 


These  Tubulars  are  made  from 
High  Grade  Steel  of  85,000  to 
90,000  Tensile  Strength. 


Separator  Bowl  Forging. 


These  Bowls  are  made  from  High  Grade  Steel  of  85,000  to  90, coo 

Tensile  Strength. 
Separator  Bowl  Forging.          Separator  Bowl  Forging. 


These  Bowls  are  made  from 
High  Grade  Steel  of  85,000 
to  90,000  Tensile  Strength. 


These  Bowls  are  made  from 
High  Grade  Steel  of  85,000 
to  90,000  Tensile  Strength. 


USEFUL  INFORMATION 


RELATING  CHIEFLY  TO 


TUBULAR  CONSTRUCTION 


COMPILED   BY 


NATIONAL  TUBE  CO. 


NATIONAL  TUBE  COMPANY 


WATER. 

Water  is  composed  of  two  gases,  hydrogen  and  oxygen, 
in  the  ratio  of  two  volumes  of  former  to  one  of  the  latter. 
It  is  never  found  pure  in  nature,  owing  to  the  readiness 
with  which  it  absorbs  impurities  from  the  air  and  soil. 
Water  boils  under  atmospheric  pressure  (14.7  Ib.)  at  212°, 
passing  off  as  steam.  Its  greatest  density  is  at  39.1°F., 
when  it  weighs  62.425  Ibs.  per  cubic  ft. 

Weight  of  Water  per  Cubic  Foot  at  Different  Temperatures. 


N 

jl 

N 

j| 

2'S 

M  0 

-O  O 

5'S 

jrl 

OJ      . 

3'^ 

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Is 

ft 

ex 

ft 

a 

ft 

32° 

62.42 

140° 

61.37 

240° 

59.10 

350° 

55.52 

460° 

51.26 

40 

62.42 

150 

61.18 

250 

58.81 

360 

55.16 

470 

50.85 

50 

62.41 

160 

60.98 

260 

58.52 

370 

54.79 

480 

50.44 

60 

62.37 

170 

60.77 

270 

58.21 

380 

54.41 

490 

50.05 

70 

62.31 

180 

60.55 

280 

57.90 

390 

54.03 

500 

49.61 

80 

62.23 

190 

60.32 

290 

57.59 

400 

53.64 

510 

49.20 

90 

62.13 

200 

60.07 

300 

57.26 

410 

53.26 

520 

48  78 

100 

62  02 

210 

59.82 

310 

56.93 

420 

52.86 

530 

48.36 

110 

61.89 

212 

59.71 

320 

56.58 

430 

52.47 

540 

47.94 

120 

61.74 

220 

59.64 

330 

56.24 

440 

52.07 

550 

47.52 

130 

61.56 

230 

59.37 

340 

55.88 

450 

51.66 

560 

47.10 

One  ft.  of  water  column  at  39°.1F  =  62.425  Ibs.  on  the  square  ft. 


=  0.0295  atmospheric  pressure 

"     "    "        "  "  "         =0.8826  in.  mercury  column  at 

32°.  F. 

"    '•    "        "  "  "         =773.3  ft.  of  air  column  at  32".F. 

and  atmospheric  pressure. 

One  Ib.  pressure  on  sq.  ft.  =  0.01602  ft.  water  column  at  39.1°F. 

"     u  "         "     "    in    -  2.307     "        '•  "        "    39.1°F. 

One  atmospheric  pressure  =•  29.92  in.  mercury  column  —  33.9  ft. 

water  column. 

One  inch  of  mercury  column  at  32°F.  =  1.133  ft    water  column. 
One  foot  of  air  column  at  32°F.  and  1  atmospheric  pressure  = 
0.001293  ft.  water  column. 


NATIONAL  TUBE  COMPANY. 


BOILER  INCRUSTATION  AND 
CORROSION. 

Water,  from  natural  sources,  as  a  rule  contains  more  or 
less  carbon  dioxide,  which  holds  in  solution  carbonates 
of  lime  and  magnesia.  On  boiling  the  water,  the  carbon 
dioxide  is  driven  out  and  the  lime  and  magnesium  in  so- 
lution are  thrown  down  in  the  form  of  a  white  or  grayish 
mud,  that  may  be  easily  removed  from  the  boiler  by 
thorough  washing.  The  presence  of  other  impurities, 
such  as  organic  matter  or  sulphate  of  lime,  is  likely  to 
make  the  deposit  hard  and  adhering. 

Sulphate  of  lime  is  more  soluble  in  cold  than  in  hot 
water,  and  is  entirely  thrown  down  at  a  temperature  of 
280°  Fahrenheit.  It  forms  a  hard  and  adhering  scale  and 
has  a  bad  effect  upon  scales  and  deposits,  composed  chief- 
ly of  carbonates. 

The  evident  treatment  of  water  containing  sulphate  of 
lime  is  to  heat  the  feed  water,  before  entering  the  boiler, 
to  a  temperature  of  at  least  280°  Fahrenheit.  This  should 
be  done  in  such  a  manner  as  to  give  time  for  the  deposi- 
tion of  the  sulphate  of  lime  when  thrown  out  of  solution. 

A  deposition  may  arise  from  the  settling  of  clay  and 
other  matter  held  in  suspension  in  the  water.  In  water 
otherwise  free  from  impurities  this  matter  commonly  de- 
posits in  the  form  of  a  soft  mud  that  may  be  easily  re- 
moved from  the  boiler.  In  conjunction,  however,  with 
other  impurities,  as,  for  example,  sulphate  of  lime,  it  may 
form  an  adhesive  scale,  in  which  case  it  is  usually  best  to 
free  the  feed  water  from  suspended  matter  by  filtration. 

In  some  cases  chemical  treatment,  either  internally  or 
externally,  should  be  resorted  to.  This  is  especially  the 
case  with  feed  waters  containing  much  free  acid,  in 
which  case  the  free  acid  should  be  neutralized  by  chem- 
ical treatment,  preferably  before  entering  the  boiler. 


NATIONAL  TUBE  COMPANY. 


If  more  than  100  parts  per  100,000  of  total  solid  residue 
be  present  in  the  water,  it  will  ordinarily  cause  trouble 
from  scale,  and  should  be  condemned  for  use  in  the 
boiler  unless  a  better  supply  be  unattainable.  Scale  re- 
duces the  efficiency  of  the  heating  surface  by  detracting 
from  the  conducting  quality  of  the  metal  and  is  apt  to 
cause  overheating  or  burning  of  the  metal,  or  even  bulg- 
ing of  the  plates  that  are  subjected  to  the  intense  heat  of 
the  furnace.  Grease,  owing  to  its  adhesive  nature,  may , 
by  collecting  impurities  contained  in  the  water,  become 
sufficiently  heavy  to  sink.  In  this  condition  it  is  apt  to 
attach  itself  to  a  plate  or  pipe  near  the  furnace  and  may, 
owing  to  its  non-conducting  qualities,  cause  serious  over- 
heating, resulting  in  burning,  bulging  or  even  blowing 
out. 

If  water  contains  more  than  5  parts  per  100,000  of  free 
sulphuric  or  nitric  acid,  serious  corrosion  will  ensue  not 
only  in  boiler  plates,  but  also  in  tubes,  pipes,  cylinders 
and  other  parts  with  which  the  steam  comes  in  contact. 

Animal  and  vegetable  oils  and  greases  decompose  into 
fatty  acids  when  subjected  to  the  temperature  of  high 
pressure  steam.  Because  of  this  their  presence  in  a  high 
pressure  steam  engine  or  boiler  will  cause  serious  corro- 
sion. 

Experiments  have  shown  that  pure  water,  into  which 
air  has  been  forced,  on  boiling  causes  corrosion. 

Highly  heated  surfaces  in  contact  with  water  contain- 
ing common  salt  corrode  and  pit  rapidly.  The  sides  of 
the  furnace,  the  tube  plates  and  the  hottest  tubes  suffer 
most. 

It  is  clear  then  that  feed- water,  free  from  solids,  com- 
bined or  in  suspension,  organic  matter,  acids  of  all  kinds, 
and  air,  would  be  best  for  the  life  of  boilers. 


NATIONAL  TUBE  COMPANY. 


TROUBLESOME 

SUBSTANCE. 


TABULAR  VIEW. 

TROUBLE. 


REMEDY  OR 
PALLIATION. 


Sediment,  mud,  clay,    Incrustation.    Filtration  ;   blowing 


etc. 
Readily  soluble  salts. 


Bicarbonatesof  lime,  j 
magnesia,  iron.        \ 


off. 
Blowing  off. 

Heating  feed.  Addi- 
tion of  caustic  soda, 
lime,  or  magnesia, 
etc. 


{Addition  of  carbon- 
ate soda,  barium 
chloride,  etc. 


Chloride  and  sul-  , 

phate    of    magne-     Corrosion. 


Carbonate  of  soda  in  )     p  .     .          (  Addition   of  barium 
large  amounts.         f    J       img<    "j      chloride,  etc. 

Acid  (in  mine  waters).      Corrosion.      Alkali. 


Dissolved     carbonic  / 
acid  and  oxygen,    l" 


Grease  (fromconden-  j 
sed  water).  j 


Organic  matter  (sew-  ) 
age).  f 


Heating  feed.  Addi- 
tion of  caustic  soda, 
slacked  lime,  etc. 


{Slacked  lime  and  filt- 
ering. 
Carbonate  of  soda. 
Substitute  mineral 
oil. 

Precipitate  with  al- 
um or  ferric  chlo- 
ride and  filter. 


Organic  matter. 


Corrosion,      Ditto. 


NATIONAL   TUBE  COMPANY. 


Analyses  in  Parts  per  J00,000  of  Water  giving  Bad  Results  in 
Steam-boilers.    (A.  K.  Hunt.) 


<U  bC 

rf-'S 

a 

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h 

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Coal-mine  water  

110 

25 

119 

39 

890 

590 

780 

30 

640 

Salt-well  

151 

38 

1  90 

48 

360 

990 

38 

21 

30 

13.10 

75 
130 

89 

'95 
161 

120 
33 

310 
210 

21 
38 

75 
70 

10 

80 

36 

Monongahela  River.. 

'•                 <k 

80 

70 

94 

81 

219 

210 

90 

32 

82 

61 

1.04 

28 

1.90 

38 

Allegheny  River  near 
Oil-works  

30 

50 

41 

68 

890 

42 

23 

In  cases  where  water  containing  large  amounts  of  total 
solid  residue  is  necessarily  used,  a  heavy  petroleum  oil, 
free  from  tar  or  wax,  which  is  not  acted  upon  by  acids  or 
alkalies,  not  having  sufficient  wax  in  it  to  cause  saponi- 
fication,  and  which  has  a  vaporizing-point  at  nearly  600° 
F.,  will  give  the  best  results  in  preventing  boiler-scale. 
Its  action  is  to  form  a  thin  greasy  film  over  the  boiler 
linings,  protecting  them  largely  from  the  action  of  acids 
in  the  water  and  greasing  the  sediment  which  is  formed, 
thus  preventing  the  formation  of  scale  and  keeping  the 
solid  residue  from  the  evaporation  of  the  water  in  such  a 
plastic  suspended  condition  that  it  can  be  easily  ejected 
from  the  boiler  by  the  process  of  "blowing  off."  If  the 
water  is  not  blown  off  sufficiently  often,  this  sediment 
forms  into  a  "putty  "  that  will  necessitate  cleaning  the 
boilers. 

Oxidation  of  pipes  may  be  prevented  by  coating  the 
pipe  with  some  protecting  material.  Galvanizing  is  coat- 
ing the  pipe  with  zinc,  which,  being  practically  unacted 
upon  by  water  from  most  natural  sources,  preserves  it. 
A  coating  of  hot  coal  tar  is  very  effective  as  a  preventive 
of  corrosion  by  fresh  or  salt  water. 


NATIONAL  TUBE  COMPANY. 


WATER  PRESSURE. 

The  pressure  of  still  water  in  pounds  per  square  inch 
against  the  sides  of  any  pipe  or  vessel  of  any  shape  what- 
ever, is  due  alone  to  the  head,  or  height  of  the  surface 
of  the  water  above  the  point  considered  pressed  upon, 
and  is  equal  to  0.434  pounds  per  square  inch  for  every 
foot  of  head.  The  fluid  pressure  per  square  inch  is  equal 
in  all  directions. 

To  find  the  total  pressure  of  quiet  water  against  and 
perpendicular  to  any  surface,  whether  vertical,  horizontal 
or  inclined  at  any  angle,  whether  it  be  flat  or  curved  ; 
multiply  together  the  area  in  square  feet  of  the  surface 
pressed,  the  vertical  depth  of  its  center  of  gravity  below 
the  surface  of  the  water,  and  the  constant  62.5.  The 
product  will  be  the  required  pressure  in  pounds.  This 
may  be  expressed  by  formula  as  follows  : 

P  =  62.5  A  D, 
In  which  P  =  the  pressure  in  pounds  of  quiescent  water  on  the 

surface  considered. 

A  =  the  area  pressed  upon  in  square  feet,  and 
D  =  the  vertical  depth  in  feet  of  center  of  gravity  of 
surface  considered. 

Pressures  in  Pounds  per  Square  Inch  in  Pipes,  Etc.,  under 
different  Heads  of  Water. 


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1 

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£sr 

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to 

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h 

£.1 

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0.43 

15 

6.49 

~29~ 

12.55 

43 

18.62 

57 

24  69 

8 

O.b6 

16 

6.93 

30 

12.99 

44 

19.05 

58 

25.12 

8 

1.30 

17 

7.36 

31 

13.42 

45 

19.49 

59 

25.55 

4 

1.73 

18 

7.79 

32 

13.86 

46 

19.92 

60 

25.99 

5 

2.16 

19 

8.22 

33 

14.29 

47 

20.35 

61 

26.42 

1 

a.  59 

20 

8.66 

34 

14.72 

48 

20.79 

62 

26.85 

7 

3.03 

21 

9.09 

35 

15.16 

49 

21.22 

63 

27.29 

8 

3.46 

22 

9.53 

36 

15.59 

50 

21.65 

64 

27.72 

9 

3.89 

23 

9.96 

37 

16.02 

51 

22.09 

65 

28.15 

10 

4.33 

24 

10.39 

38 

16.45 

52 

22.52 

66 

28  58 

11 

4.76 

25 

10.82 

39 

16.89 

53 

22.95 

67 

29.02 

19 

5.20 

26 

11.26 

40 

17.32 

54 

23.39 

68 

29.45 

18 

5.63 

27 

11.69 

41 

17.75 

55 

23.82 

69 

29  88 

14 

6.06 

28 

12.12 

42 

18.19 

56 

24.26 

70 

30.32 

100                      NATIONAL  TUBE  COMPANY. 

Pressures  in  Pounds  per  Square  Inch  in  Pipes,  Etc,,  under 
different  Heads  of  Water. 

(CONTINUED.) 

1 

s-s 

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fa 

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M 

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IH      • 

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8 

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s 

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35 

11 

w  rt 

V 

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0)  3 

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to 

££ 

to 

£sr 

£ 

££ 

to 

to 

££ 

71 

30.75 

121 

52.41 

171 

74.07 

221 

95.73 

271 

117.39 

72 

31.18 

122 

52.84 

172 

74.50 

222 

96.16 

272 

117.82 

73 

31.62 

123 

53.28 

173 

74.94 

223 

96.60 

273 

118.26 

74 

32.05 

124 

53.71 

174 

75.87 

224 

97.03 

274 

118.69 

75 

32.48 

125 

54.15 

175 

75.80 

225 

97.46 

275 

119.12 

76 

32.92 

126 

54.58 

176 

76.23 

226 

97.90 

276 

119.56 

77 

33.35 

127 

55.01 

177 

76.67 

227 

98.33 

277 

119.99 

78 

33.78 

128 

55.44 

178 

77.10 

228 

98.76 

278 

120.42 

79 

34.21 

129 

55.88 

179 

77.53 

229 

99.20 

279 

120.85 

80 

34.65 

130 

56.31 

180 

77.97 

230 

99.63 

280 

121.29 

81 

35.08 

131 

56.74 

181 

78.40 

231 

100.06 

281 

121.72 

82 

35.52 

132 

57.18 

182 

78.84 

232 

100.49 

282 

122.15 

83 

35.95 

133 

57.61 

183 

79.27 

233 

100.93 

283 

122.59 

84 

36.39 

134 

58.04 

184 

79.70 

234 

101.36 

284 

123.02 

85 

36.82 

135 

58.48 

185 

80.14 

235 

101.79 

285 

123.45 

86 

37.25 

136 

58.91 

186 

80.57 

236 

102.23 

286 

123.89 

87 

37.68 

137 

59.34 

187 

81.00 

237 

102.66 

287 

124.32 

88 

38.12 

138 

59.77 

188 

81.43 

238 

103.09 

288 

124.75 

89 

38.55 

139 

60.21 

189 

81.87 

239 

103.53 

289 

125.18 

90 

38.98 

140 

60.64 

190 

82  30 

240 

103.96 

290 

125.62 

91 

39.42 

141 

61.07 

191 

82.73 

241 

104.39 

291 

126.05 

92 

39.85 

142 

61.51 

192 

83.17 

242 

104.83 

292 

126.48 

93 

40.28 

143 

61.94 

193 

83.60 

243 

105.26 

293 

126.92 

94 

40.72 

144 

62.37 

194 

84.03 

244 

105.69 

294 

127.35 

95 

41.15 

145 

62.81 

195 

84.47 

245 

106.13 

295 

127.78 

96 

41.58 

146 

63.24 

196 

84.90 

246 

106.56 

296 

128.22 

97 

42.01 

147 

63.67 

197 

85.33 

247 

106.99 

297 

128.65 

98 

42.45 

148 

64.10 

198 

85.76 

248 

107.43 

298 

129.08 

99 

42.88 

149 

64.54 

199 

86.20 

249 

107.86 

299 

129.51 

100 

43.31 

150 

64.97 

200 

86.63 

250 

108.29 

300 

129.95 

43.75 

151 

65.40 

201 

87.07 

251 

108.73 

310 

134.28 

102 

44.18 

152 

65.84 

202 

87.50 

252 

109.16 

320 

138.62 

103 

44.61 

153 

66.27 

203 

87.93 

253 

109.59 

330 

142.95 

104 

45.05 

154 

66.70 

204 

88.36 

254 

110.03 

340 

147.28 

105 

45.48 

155 

67.14 

205 

88.80 

255 

110.46 

350 

151.61 

106 

45.91 

156 

67.57 

206 

89.23 

256 

110.89 

360 

155.94 

107 

46.34 

157 

68.00 

207 

89.66 

257 

111.32 

370 

160.27 

108 

46.78 

158 

68.43 

208 

90.10 

258 

111.76 

380 

164.61 

109 

47.21 

159 

68.87 

209 

90.53 

259 

112.19 

390 

168.94 

110 

47.64 

160 

69.31 

210 

90.96 

260 

112.62 

400 

173.27 

111 

48.08 

161 

69.74 

211 

91.39 

261 

113.06 

500 

216.58 

112 

48.51 

162 

70.17 

212 

91.83 

262 

113.49 

600 

259.90 

113 

48.94 

163 

70.61 

213 

92.26 

263 

113.92 

700 

303.22 

114 

49.38 

164 

71.04 

214 

92.69 

264 

114.36 

800 

346.54 

115 

49.81 

165 

71.47 

215 

93.13 

265 

114.79 

900 

389.86 

116 

50.24 

166 

71.91 

216 

93  56 

266 

115.22 

1000 

433.18 

117 

50.68 

167 

72.34 

217 

93.99 

267 

115.66 

118 

51.11 

168 

72.77 

218 

94.43 

268 

116.09 

119 

51.54 

169 

73.20 

219 

94.86 

269 

116.52 

120 

51.98 

170 

73.64 

220 

95.30 

270 

116.96 

NATIONAL  TUBE  COMPANY: 


FLOW  OF  WATER  IN  PIPES. 

The  vertical  height  of  the  source  of  water  above  the 
outlet  is  called  the  head.  The  greater  the  head  the 
greater  will  be  the  velocity  of  efflux  if  the  length  and  di- 
ameter of  the  pipe  remain  constant. 

To  find  the  velocity  of  water  discharged  from  a  pipe  line 
longer  than  4  times  its  diameter,  knowing  the  head, 
length  and  inside  diameter,  use  the  following  formula  : 


In  which    v  =  approximate  mean  velocity  in  feet  per  second, 
m  =  coefficient  from  table  below, 
d   =  diameter  of  pipe  in  feet, 
h  =  total  head  in  feet, 
L  =  total  length  of  line  in  feet. 

VALUES  OF  COEFFICIENT  M. 


hd 

DIAMETER  OF  PIPE  IN  FEET. 

0.05 

0.10 

0.50 

1 

1.5 

2 

3 

4 

Iv+54d 

0.005 
0.01 
0.02 
0.03 
0.05 
0.10 
0.20 

M 
29 
34 
39 
41 
44 
47 
48 

M 
31 
35 

40 
43 
47 
50 
51 

M 
33 
37 
42 
47 
52 
54 
55 

M 
35 
39 
45 
50 
54 
56 
58 

M 
37 
42 

49 
54 
56 

58 
60 

M 
40 
45 
52 
57 
60 
62 
64 

M 
44 
49 
56 
60 
64 
66 
67 

M 
47 
53 
59 
63 
67 
70 
70 

The  above  coefficients  are  averages  deduced  from  a 
large  number  of  experiments.  In  most  cases  of  pipes 
carefully  laid  and  in  fair  condition,  they  should  give 
results  within  5  to  10  per  cent,  of  the  truth. 

Example. — Given  the  head,  h  —  50  ft. ;  the  length, 
Z,  =  5280  ft.;  and  the  diameter,  d  =  2  ft.;  to  find  the 
velocity  and  quantity  of  discharge. 


NATIONAL  TUBE  COMPANY. 


Substituting  these  values  in  above  formula,  we  get : 

/innr     /  2Xso      /w 

T   L+54d  =  r   2580+108  —  T   5388  =  u>1*0' 


In  column  headed  A/    hd      find  0.10,  which  is  the 
*    L/+54d 

value  nearest  to  0.136,  and  look  along  this  line  until 
column  headed  "  2  "  is  reached,  then  read  62  as  the  value 
of  coefficient  ra. 

Then  v  =  62x0.136  =  8.432  ft.  per  sec.,  the  required 
velocity. 

To  find  the  discharge  in  cu.  ft.  per  sec.,  multiply  this 
velocity  by  area  of  cross  section  of  pipe  in  sq.  ft. 

Thus,  3. 1416  x  (I)2  x  8.432  =  26.49  cu.  ft.  per  sec. 

Since  there  are  7.48  gal.  in  a  cu.  ft.,  the  discharge  in 
gal.  per  sec.  =  26.49x7. 48  =  198.2. 

The  above  formula  is  only  an  approximation,  since  the 
flow  is  modified  by  bends,  joints,  incrustations,  etc. 
Wrought  Iron  and  Steel  Pipes  are  smoother  than  cast 
iron  ones,  thereby  presenting  less  friction  and  less  en- 
couragement for  deposits  ;  and,  being  in  longer  lengths, 
the  number  of  joints  is  reduced,  thus  lessening  the 
undesirable  effects  of  eddy  currents. 

To  find  the  head  in  feet  necessary  to  give  a  stated  dis- 
charge in  cu.  ft.,  use  the  formula.* 

,.0.000704  Q2  (L+54d) 
d5 

In  which  h  =  total  head  in  feet, 

L  =  total  length  of  line  in  feet, 

d  =  diameter  of  pipe  in  feet, 

Q  =  quantity  of  water  in  cu.  ft.  per  second. 

Example. — Given  the  diameter  of  pipe,  ^=0.5  ft.;  the 
length  of  pipe,  L  —  20  ft. ;  and  the  quantity  of  water  to 
be  discharged,  #-  =  3.07  cu.  ft.  per  sec.;  to  find  the  neces- 
sary head. 


NATIONAL  TUBE  COMPANY. 


Substituting  these  values  in  the  above  formula,*  we  get : 

0.000704  x  9.4  x  (20+27) 
(0.5)' 

=  0.000704^9.4x47 

The  following  formula*  is  simpler  and  can  be  used  when 
54  d  in  relation  to  L  is  so  small  as  to  be  negligible. 

0.000704  Q8  x  L 
— d^ 

If  the  pipe,  instead  of  being  straight,  has  easy  curves 
(say  with  radius  not  less  than  5  diameters  of  the  pipe) 
either  horizontal  or  vertical,  the  discharge  will  not  be 
materially  diminished,  so  long  as  the  total  heads,  and 
total  actual  lengths  of  pipe  remain  the  same,  but  it  is  ad- 
visable to  make  the  radius  as  much  more  than  5  diameters 
as  can  conveniently  be  done. 

To  find  the  diameter  of  a  pipe  ^bf  given  length  to  de- 
liver a  given  quantity  of  water  under  a  given  head,  use 
the  following : 


=  0.234 


fi 


In  which  d  —  diameter  of  pipe  in  feet, 

Q  —  cu.  ft.  per  second  delivered, 
L  —  length  of  line  in  feet, 
h  —  head  in  feet. 

Example. — Given  the  head,  h  —  700  feet ;  the  length  of 
pipe,  L— 3000  feet;  the  quantity  to  be  delivered,  Q-4 
cu.  ft.  per.  sec. ;  required  the  diameter  of  pipe  necesssary. 

Substituting  these  values  in  the  above  formula,*  we 
get: 

d=0.234    A/  16x3000=0.234    4/68.57=0.545  ft.=6.54  in. 


NATIONAL  TUBE  COMPANY. 


The  diameter  of  a  pipe  may  also  be  found  by  using  the 
following  formula  :  * 


=  125 


In  which  D  =  diameter  of  pipe  in  inches, 

q  =  gallons  per  second, 
"  L  =  length  of  line  in  feet, 
h  =  head  in  feet. 


If,  in  formula  v  =  m.\/      x —  we  substitute 
V   Iy-}-54d 

average  value  for  m,  we  get : 


dxh 


The  following  table,  calculated  by  the  above  formula 
shows  the  velocities  and  discharges  through  a  pipe  one 
mile  long  and  one  foot  in  diameter,  under  different  heads. 
But  they  will  be  very  nearly  the  same  for  any  greater 
lengths  ;  and  also  quite  approximate  for  shorter  ones  not 
less  than  1000  or  even  500  diameters  long,  provided  that 
in  all  cases  they  have  the  same  RATE;  OF  HEAD  ;  that  is,  if 
the  given  pipe  of  one  foot  diameter  is  2  or  3  miles  long, 
it  must  have  2  or  3  times  as  much  head  as  the  pipe  in  the 
table  in  order  to  have  very  nearly  the  same  velocity  and 
discharge. 


*  When  solving  examples  by  the  use  of  these  formulas  use 
the  table  of  Fifth  Powers  and  Fifth  Roots.  Solutions  may  also 
be  easily  effected  by  the  use  of  logarithms. 


NATIONAL  TUBE  COMPANY.                      105 

The  velocities  and  discharges  through  a  straight,  smooth 

pipe  one  foot  in  diameter,  and  one  mile  or  5280  diameters 

in  length* 

Head  in 
feet  per 
100  feet. 

Head  in 
feet 
per  mile. 

Velocity  in 
feet  per 
second. 

Discharge 
in  cubic  feet 
per  second. 

Discharge 
in  cubic  feet 
per  24  hours. 

.0019 

.1 

.208 

.1633 

14,114 

.0038 

.2 

.293 

.2301 

19,880 

.0057 

.3 

.359 

.2819 

24,360 

.0076 

.4 

.415 

.3267 

28,229 

.0095 

.5 

.464 

.3638 

31,435 

.0114 

.6 

.508 

.3989 

34,464 

.0132 

.7 

.549 

.4311 

37,247 

.0151 

.8 

.585 

.4602 

39,760 

.0170 

.9 

.623 

.4901 

42,343 

.0189 

1. 

.656 

.5144 

44,431 

.0237 

.25 

.735 

.5753 

49,701 

.0284 

.5 

.805 

.6322 

54,604 

.0331 

.75 

.871 

.6832 

59,011 

.0379 

2. 

.928 

.7276 

62,870 

.0426 

.25 

.984 

.7696 

66,484 

.0473 

.5 

1.04 

.8168 

70,572 

.0521 

.75 

1.08 

.8482 

73,284 

.0568 

3. 

1  13 

.8914 

76,982 

.0758 

4. 

1.31 

1.028 

88,862 

.0947 

5. 

1.47 

1.150 

99,403 

.1136 

6. 

1.61 

1.264 

109,209 

.1325 

7. 

1.74 

1.366 

118,022 

.1514 

8. 

1.86 

1.455 

125,740 

.1703 

9. 

1.96 

1.539 

132,969 

.1894 

10. 

2.08 

1.633 

141,145 

.2273 

12. 

2.27 

1.782 

153,964 

.2652 

14. 

2.45 

1.924 

166,233 

.3030 

16. 

2.62 

2.057 

177,724 

.3409 

18. 

2.78 

2.183 

188,611 

.3',  88 

20. 

2.93 

2.301 

198,806 

.4735 

25. 

3.28 

2.572 

222,156 

.5682 

30. 

3.59 

2.819 

243,604 

.6629 

35. 

3.88 

3.047 

263,260 

.7576 

40. 

4.15 

3.267 

282,288 

.8523 

45. 

4.40 

3-451 

298,209 

.9470 

50. 

4.64 

3.638 

314,352 

1.136 

60. 

5.08 

3.989 

344,649 

1.326 

70. 

5.49 

4.311 

372,470 

1.515 

80. 

5.85 

4.602 

397,613 

E  ^  P  i 

106                      NATIONAL  TUBE  COMPANY. 

The  velocities  and  discharges  through  a  straight,  smooth 

pipe  one  foot  in  diameter,  and  one  mile  or  5280  diameters 

in  length. 

Head  in 
feet  per 

Head  in 
feet 

Velocity  in 
feet  per 

Discharge 
in  cubic  feet 

Discharge 
in  cubic  feet 

100  feet. 

per  mile. 

second. 

per  second. 

per  24  hours. 

1.704 

90. 

6.23 

4.900 

423,435 

1.894 

100. 

6.56 

5.144 

444,312 

2.083 

110. 

6.87 

5.395 

466,128 

2.272 

120. 

7.18 

5.639 

487,209 

2.462 

130. 

7.47 

5.866 

506,822 

2.652 

140. 

7.76 

6.094 

526,521 

2.841 

150. 

8.05 

6.322 

546,048 

3.030 

160. 

8.30 

6.534 

564,576 

3.219 

170. 

8.55 

6.715 

580,176 

3.408 

180. 

8.80 

6.903 

596,418 

3.596 

190. 

9.04 

7.100 

613,440 

3.788 

200. 

9.28 

7.276 

628,704 

4.261 

225. 

9.84 

7.696 

664,848 

4.735 

250. 

10.4 

8.168 

705,728 

5.208 

275. 

10.8 

8.482 

732,844 

5.682 

300. 

11.3 

8.914 

769,824 

6.629 

350. 

12.3 

9.621 

831,168 

7.576 

400. 

13.1 

10.28 

888,624 

8.532 

450. 

13.9 

10.91 

943,056 

9.47 

500. 

14.7 

11.50 

994,032 

10.41 

550. 

15.4 

12.09 

1,044,576 

11.36 

600. 

16.1 

12.64 

1,092,096 

12.30 

650. 

16.7 

13.11 

1,132,704 

13.25 

700. 

17.4 

13.66 

1,180,224 

14.20 

750. 

18.0 

14.13 

1,220,832 

15.15 

800. 

18.6 

14.55 

1,257,408 

16.09 

850. 

19.1 

15.00 

1,296,000 

17.04 

900. 

19.6 

15.39 

1,329,696 

17.99 

950. 

20.3 

15.94 

1,377,216 

18.94 

1000. 

20.8 

16.33 

1,411,456 

22.73 

1200. 

22.7 

17.82 

1,539,648 

26.52 

1400. 

24.5 

19.24 

1,662,336 

30.30 

1600. 

26.2 

20.57 

1,777,248 

34.08 

1800. 

27.8 

21.83 

1,886,112 

37.87 

2000. 

29.3 

23.01 

1,988,064 

47.35 

2500. 

32.8 

25.72 

2,221,560 

56.81 

3000. 

35.9 

28.19 

2,436,040 

NATIONAL  TUBE  COMPANY.  107 

Head  is  the  vertical  distance  from  the  surface  of  the 
water  in  the  reservoir  to  the  center  of  gravity  of  the 
lower  end  of  the  pipe  when  the  discharge  is  into  the  air  ; 
or  to  the  level  surface  of  the  lower  reservoir  when  the 
discharge  is  under  water. 

To  reduce  cubic  feet  to  U.  S.  Gallons,  multiply  by  7.48. 

To  find  either  the  area  of  pipe,  the  mean  velocity,  or  the 
quantity  discharged,  when  the  other  two  are  given,  use  the 


ischarge  in  cubic  feet  per  second, 
Area  in  square  feet  =    Mean  velocity  in  feet  per  second. 


Mean  velocity  in  _  Discharge  in  cubic  feet  per  second, 
feet  per  second.   .  Area  in  square  feet. 


Discharge  in  cubic  feet         Area  in          Mean  velocity  in 
per  second.  square  f  eet  A  feet  per  second. 


[The  terms  may  be  in  inches  instead  of  feet ;  and  in 
minutes  or  hours  instead  of  seconds.] 

For  the  diameter  of  a  long  pipe  required  to  deliver  either 
more  or  less  water  than  that  of  a  J  foot  diameter,  and  under 
the  same  rate  of  inclination,  or  of  head  in  feet  per  mile,  see 
table  on  next  page. 

The  use  of  this  table  is  not  sufficiently  correct  for  pipes 
less  than  about  1,000  (or  at  furthest  500)  diameters  long. 


~» 

108                      NATIONAL  TUBE  COMPANY. 

S, 

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To  find  the  discharge  from  a  pipe  (not  less  than  1,000, 

or  at  least  500  times  its  own  diameter  in  length)  when 

the  head  is  given,  take  from  the  first  table  the  discharge 

through  a  pipe  one  ft.  in  diameter  for  the  given  head, 

and  divide  the  required  discharge  by  this  tabular  one; 

then  look  for  the  quotient  in  the  column  of  the  second 

table,  headed  "Ratio  of  Discharge,"  and  opposite  it,  in 

columns  1  and  2,  will  be  found  the  required  diameter. 

. 

NATIONAL  TUBE  COMPANY. 


From  this  table  we  see  that  a  14  inch  pipe  will  deliver 
nearly  1J^  times  as  much  as  a  12  inch  pipe,  and  a  16  inch 
one  fully  twice  as  much  as  a  12  inch,  all  having  the  same 
length  and  head. 

EXAMPLE. — Having  given  the  head  from  a  reservoir 
to  a  certain  point  of  delivery,  as  20  ft.  in  a  distance  of 
1,860  ft.,  what  must  be  the  diameter  of  a  pipe  to  deliver 
6  cubic  feet  of  water  per  second  ? 

We  find  that  a  fall  of  20  ft.  in  1,860,  is  equal  to  a  fall 
of  1.075  ft.  in  100;  or  1,860:  20  =  100:  1.075.  Then  we  see 
by  the  first  table  that  with  a  fall  of  1.075  ft.  in  100,  a 
long  pipe  of  1  ft.  diameter  discharges  about  3.8  cubic 
feet  per  second.  But  we  want  6  —  1.58  times  as  much 
as  the  1  ft.  pipe  can  deliver  ;  then  by  the  second  table, 
we  see  that  the  pipe  to  do  this,  under  the  same  rate  of 
head,  must  be  about  14^  in.  in  diameter.  In  practice 
we  should  adopt  at  least  15  in. 


NATIONAL  TUBE  COMPANY. 


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NATIONAL  TUBE  COMPANY. 


EXAMPLE.—  Given  120  feet  head  and  600  feet  length 
of  18  inch  pipe,  discharging  3500  gallons  per  minute  :  To 
find  effective  head:  Look  in  column  headed  "18  inch 
Pipe,"  and  opposite  3500  in.  first  column  read  "4.7  ft." 
(which  is  the  loss  of  head  by  friction  for  an  18  in.  pipe 
1000  ft.  long),  and  multiplying  this  by  600/1000,  or  0.6, 
we  get  2.82  ft.,  the  loss  of  head.  The  effective  head  re- 
quired then  equals  120  ft.  less  2.8  ft.  or  117.2  ft. 


Flow  of  Water  in  Pipes  for  a  Velocity  of  JOO  Ft.  per  Minute. 


Diameter 
in 
Inches. 

Area  in 
Square 
Feet. 

Flow  in 
Cubic  Feet 
perMinute. 

Flow  in  U.  S. 
Gallons  per 
Minute. 

Flow  in 
U.S.  Gallons 
per  Hour. 

% 

.00077 

0.077 

.57 

34 

i/ 

.00136 

0.136 

1.02 

61 

X 

.00307 

0.307 

2.30 

138 

1 

.00545 

0.545 

4.08 

245 

1% 

.00852 

0.852 

6.38 

383 

*# 

.01227 

1.227 

9.18 

551 

W 

.01670 

1.670 

12.50 

750 

2 

.02182 

2.182 

16.32 

979    ' 

&A 

.0341 

3.41 

25.50 

1,530 

3 

.0491 

4.91 

36.72 

2,203 

4 

.0873 

8.73 

65.28 

3,917 

5 

.136 

13.6 

102.00 

6,120 

6 

.196 

19.6 

146.88 

8,813 

7 

.267 

26.7 

199.92 

11,995 

8 

.349 

34.9 

261.12 

15,667 

9 

.442 

44.2 

330.48 

19,829 

.  10 

.545 

54.5 

408.00 

24,480 

11 

.660 

66.0 

493.68 

29,621 

12 

.785 

78.5 

587.52 

35,251 

To  find  the  quantity  in  gallons  a  pipe  will  deliver,  the 
velocity  of  flow  being  100  ft.  per  minute  :  Square  the  di- 
ameter in  inches  and  multiply  by  4.08. 


8*  '  IB 

NATIONAL  TUBE  COMPANY.                     118 

Flow  of  Water  in  House-service  Pipes. 

(Thomson  Meter  Co.) 

Condition 
of 
Discharge. 

2-g 
3-3 

SST 

ij 

Z£ 

Discharge  in  Cubic  Feet  per  Minute  from 
the  Pipe. 

Nominal  Diameters  of  Iron  or  Lead  Ser- 
vice-pipe in  Inches. 

M 

% 

¥4 

1 

1^ 

2 

3 

4 

6 

Through  35 
feet  of 
service- 

ESno 

pressure. 

30 
40 
50 
60 
75 
100 
130 

1.10 
1.27 
1.42 
1.56 
1.74 
2.01 
2.29 

.92 
2.22 
2.48 
2.71 
3.03 
3.50 
3.99 

3.01 
3.48 
3  89 
4.26 
4.77 
5.50 
6.28 

6.13 
7.08 
7.92 
8.67 
9.70 
11.20 
12.77 

16.58 
19.14 
21.40 
23.44 
26.21 
30.27 
34.51 

33.34 
38.50 
43.04 
47.15 
52.71 
60.87 
69.40 

88.16 
101.80 
13.82 
24.68 
139.39 
160.96 
183.52 

173.85 
200.75 
224.44 
245.87 
274.89 
317.41 
361.91 

444.63 
513.42 
574.02 
628.81 
703.03 
811.79 
925.58 

Through 
100  feet  of 
service- 
pipe,  no 
back 
pressure. 

80 
40 
50 
GO 
75 
100 
130 

0.66 
0.77 
0.86 
0.94 
1.05 
1.22 
1.39 

0.55 
0.66 
0.75 
0.83 
0.94 
1.10 
1.26 

1.16 
1.34 
1.50 
1.65 
1.84 
2.13 
2.42 

1.84 
2.12 
2.37 
2.60 
2.91 
3.36 
3.83 

3.78 
4.36 
4.88 
5.34 
5.97 
6.90 
7.86 

10.40 
12.01 
13.43 
14.71 
16.45 
18.99 
21.66 

21.30 
24.59 
27.50 
30.12 
33.68 
38.89 
44.34 

58.19 
67.19 
75.13 
82.30 
92.01 
106.24 
121.14 

118.13 
136.41 
152.51 
167.06 
186.78 
215.68 
245.91 

317.23 
366.30 
409.54 
448.63 
501.58 
579.18 
660.36 

Through 
100  feet  of 
service- 
pipe,  and 
15  feet 
vertical 
rise. 

30 
40 
50 
60 
75 
100 
130 

0.90 
1.15 
1.31 
1.45 
1.64 
1.92 
2.20 

1.52 
1.81 
2.06 
2.29 
2.59 
3.02 
3.48 

3.11 
3.72 
4.24 
4.70 
5.32 
6.21 
7.14 

8.57 
10.24 
11.67 
12.94 
14.64 
17.10 
19.66 

17.55 
20.95 
23.87 
26.48 
29.96 
35.00 
40.23 

47.90 
57.20 
65.18 
72.28 
81.79 
95.55 
109.82 

97.17 
116.01 
132.20 
146.61 
165.90 
193.82 
222.75 

260.56 
311.09 
354.49 
393.13 
444.85 
519.72 
597.31 

Through 
100  feet  o 
service- 
pipe,  and 
30  feet 
vertical 
rise. 

3C 
4C 
« 

6C 

7£ 
IOC 
13( 

0.44 
0.55 
0.65 

0.73 
0.84 
1.00 
1.15 

0.77 
0.97 
1.14 
1.28 
1.47 
1.74 
2.02 

1.22 
1.53 
1.79 
2.02 
2  32 
2.75 
3.19 

2.50 
3.15 
3.69 
4.15 
4.77 
5.65 
6.55 

6.80 
8.68 
10.16 
11.45 
13.15 
15.58 
18.07 

14.11 
17.79 
20.82 
23.47 
26.95 
31.93 
37.02 

38.63 
48.68 
56.98 
64.22 
73.76 
87.38 
101.33 

78.54 
98.98 
115.87 
130.59 
149.99 
177.67 
206.04 

211.54 
266.59 
312.08 
351.73 
403.98 
478.55 
554.96 

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NATIONAL  TUBE  COMPANY.                      115 

'  SAFE  PRESSURES  AND  EQUIVALENT  HEADS  OF  WATER  FOR  CAST  IRON  PIPE  OF 
DIFFERENT  SIZES  AND  THICKNESSES. 
(Calculated  by  F.  H.  Lewis,  from  Fanning's  Formula.) 

SIZE  OF  PIPE. 

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NATIONAL  TUBE  COMPANY.                      117 

WEIGHTS  OF  CAST  IRON  PIPE  TO  LAY  12  FEET 
LENGTHS. 
Weights  are  in  Pounds  and  include  Hub. 
(Calculated  by  F.  H.  Lewis.) 

Thickness. 

Inside  Diameter. 

Inches. 

Equiv. 
Decimals. 

4" 

6" 

8" 

10" 

12" 

14" 

16" 

18" 

20" 

.375 
.40625 
.4375 
.4687 
.5 
.53125 
.5625 
.59375 
.625 
.6875 
.75 
.8125 
.875 
.9375 
1. 
1.125 
1.25 
1.375 

209 
828 
247 
968 
286 
806 
887 

30  1 
331 

35s 

38(5 
414 
442 
470 
498 

400 
435 
470 
505 
541 
577 
013 
OKI 
080 

581 
621 

008 
712 
750 

soi 

H45 
935 
1020 

092 
744 
795 
8-10 
899 
951 
1003 
1110 
1216 
1321 
1  132 

804 
968 

922 
983 

1013 
1103 
1163 
12S5 

1  IDS 

1531 
L656 
L788 

1909 

1050 
1118 
1186 
1254 
1322 
1460 
1598 
1738 
1879 
2021 
2163 

1177 
1253 
1329 
1405 
1481 
1635 
1789 
1945 
2101 
2259 
2418 
2738 
3002 

1640 
1810 
1980 
2152 
2324 
2498 
2672 
3024 
3380 

Thickness. 

Inside  Diameter. 

Inches. 

Equiv. 
Decimals. 

W 

84- 

27- 

30' 

33" 

36" 

42" 

48" 

60' 

If 
i 

I 

\ 

i 

.625 
.6875 
.75 
.8125 
.875 
.9375 
1. 
1.125 
1.25 
1.375 
1.5 
1.625 
1.75 
1.875 
2. 
2.25 
2.5 
2.75 

1799 
1985 
2171 
B859 

2547 
2737 
8927 

:;:!!(  > 
3698 

2100 

2362 
2505 
2769 
2975 
3180 
3598 

to  10 

1139 

2  122 

26  IS 
2875 
3  in:; 
3332 
3562 
4027 
1  192 
1961 
5139 

-.'93  1 
3180 
3137 
3090 
3912 
1  15(1 
1970 
5191 
6012 
0539 

3221 
3490 

3771 
10  IS 
1325 
4880 
5147 
6015 
65X1 
7  I.V.I 
7737 

.•5507 
3S06 
1105 
1106 
4708 
531  « 
592  1 
6510 
715S 
7782 
8405 

4426 
4773 
5122 
5472 
6176 
6880 
7591 
8303 
9022 
9742 
10468 
11197 

6442 
5839 
6236 
7034 
7833 
8640 
9447 
10260 
11076 
11898 
12725 
14385 

9742 
10740 
11738 
12744 
13750 
14763 
15776 
17821 
19880 
21956 

H_ 

118                     NATIONAL  TUBE  COMPANY. 

Contents  in  Cubic  Feet  and  U.  S.  Gallons  of  Pipes  and 

Cylinders  of  Various  Diameters  and  One  Foot  in  Length. 

1  gallon=231  cubic  inches.    1  cubic  foot=7.4805  gallons. 

For  1  Foot  in 

For  1  Foot  in 

For  1  Foot  in 

'H  • 

Length. 

V     u* 

Length. 

•••     . 

Length. 

§•1 

Cubic  ft. 

U.S. 

*»  "5 

G   a 

Cubic  Ft. 

U.S. 
Gals. 

a  is 

CubicTt. 

U.S. 
Gals. 

P 

in  Sq.  ft 

231 
Cu.  In. 

Q 

a  so  Area 
in  Sq.  Ft. 

231 
Cu.  In. 

S~ 

also  Area 
inSq.  Ft. 

231  ' 
Cu.  In. 

M 

.0003 

.0025 

6M 

.2485 

1.859 

19 

1.969 

14.73 

j^ 

.0005 

.004 

7 

.2673 

1.999 

2.074 

15.51 

•2 

.0008 

.0057 

7^4 

.2867 

2.145 

20 

2.182 

16.32 

TS 

.001 

.0078 

71^3 

.3068 

2.295 

20^ 

2.292 

17  15 

(2 

.0014 

.0102 

7% 

.3276 

2.45 

21 

2.405 

17.99 

1% 

.0017 

.0129 

8 

.3491 

2.611 

21/4 

2.521 

18.86 

IB 

.0021 

.0159 

8*4 

.3712 

2.777 

22 

2.640 

19.75 

11 

.0026 

.0193 

giz 

.3941 

2.948 

22J4 

2.761 

20.66 

a^ 

.0031 

.0230 

834 

.4176 

3.125 

23 

2.885 

21.58 

n 

.0036 

.0269 

9 

.4418 

3.305 

23J4 

3.012 

22.53 

7<C 

.0042 

.0312 

9M 

.4667 

3.491 

24 

3.142 

23.50 

n 

.0048 

.0359 

9^s 

.4922 

3.682 

25 

3.409 

25.50 

1 

.0055 

.0408 

9% 

.5185 

3.879 

26 

3.687 

27.58 

1/4 

.0085 

.0638 

10 

.5454 

4.08 

27 

3.976 

29.74 

1}^ 

.0123 

.0918 

.5730 

4.286 

28 

4.276 

31.99 

1% 

.0167 

.1249 

10*2 

.6013 

4.498 

29 

4.587 

34.31 

2 

.0218 

.1632 

1034 

.6303 

4.715 

30 

4.909 

36.72 

.0276 

.2066 

11 

,   .66 

4.937 

31 

5.241 

39.21 

2^2 

.0341 

.2550 

11U 

.6903 

5.164 

32 

5.585 

41.78 

2% 

.0412 

.3085 

.7213 

5.396 

33 

5.940 

44.43 

3 

.0491 

.3672 

HM 

.7530 

5.633 

34 

6.305 

47.16 

3J4 

.0576 

.4309 

12 

.7854 

5.875 

35 

6.681 

49.98 

3^1 

.0668 

.4998 

.8522 

6.375 

36 

7.069 

52.88 

3% 

.0767 

.5738 

13 

.9218 

6.895 

37 

7.467 

55.86 

4 

.0873 

.6528 

.994 

7.436 

38 

7.876 

58.92 

4J4 

.0985 

.7369 

14 

1.069 

7.997 

39 

8.296 

62.06 

48 

.1134 

.8263 

1.147 

8.578 

40 

8.727 

65.28 

4% 

.1231 

.9206 

15  3 

.227 

9.180 

41 

9.168 

68.58 

5 

.1364 

1.020 

15^ 

.310 

9.801 

42 

9.621 

71.97 

.1503 

1.125 

16 

.396 

10.44 

43 

10.085 

75.44 

51^ 

.1650 

1.234 

16*4 

.485 

11.11 

44 

10.559 

78.99 

5*& 

.1803 

1.349 

.576 

11.79 

45 

11.045 

82.62 

6 

.1963 

1.469 

17J4 

.670 

12.49 

46 

11.541 

86.33 

.2131 

1.594 

18 

.768 

13.22 

47 

12.048 

90.13 

6*J 

.2304 

1.724 

.867 

13.96 

48 

12.566 

94.00 

To  find  the  capacity  of  pipes  greater  than  those  given,  look  in 

the  table  for  a  pipe  of  one  half  the  given  size,  and  multiply  its 

capacity  by  4  ;  or  one  of  one  third  its  size,  and  multiply  its  capac- 

ity by  9,  etc. 

To  find  the  weight  of  water  in  any  of  the  given  sizes  multiply 

the  capacity  in  cubic  feet  by  the  weight  of  a  cubic  foot  of  water 

at  the  temperature  of  the  water  in  the  pipe. 

To  find  the  capacity  of  a  cylinder  in  U.  S.  gallons,  multiply  the 

length  by  the  square  of  the  diameter  and  by  0.0034. 

NATIONAL  TUBE  COMPANY.                      119 

CYLINDRICAL  VESSELS,  TANKS,  CISTERNS,  ETC. 

Diameter  in  Feet  and  Inches,  Area  in  Square  Feet,  and 

U.  S.  Gallons  Capacity  for  One  Foot  in  Depth. 

1  gallon  =  231  cubic  inches  =  0.1337  cubic  foot. 

Diam. 

Area. 

Gals. 

Diam. 

Area. 

Gals. 

Diam. 

Area. 

Gals. 

Ft.  In. 

Sq.ft. 

One  foot 
depth. 

Ft.  In. 

Sq.  ft. 

One  foot 
depth. 

Ft.  In. 

Sq.  ft. 

One  foot 
depth. 

1 

.785 

5.87 

3      4 

8.727 

65.28 

5       8 

25.22 

188.66 

1       1 

.922 

6.89 

3      5 

9.168 

68.58 

5     9 

25.97 

194.25 

1       2 

1.069 

8.00 

3      6 

9.621 

71.97 

5    10 

26.73 

199.92 

1       3 

1.227 

9.18 

3      7 

10.085 

75.44 

5    11 

27.49 

205.67 

1      4 

1.396 

10.44 

3      8 

10.559 

78  99 

6 

28.27 

211.51 

1      5 

1.57S 

11.79 

3      9 

11.045 

82.62 

6      3 

30.68 

229.50 

1      6 

1.767 

13.22 

3    10 

11.541 

86.33 

6      6 

33.18 

248.23 

1      7 

1.969 

14.73 

3    11 

12.048 

90.13 

6      9 

35.78 

267.69 

1      8 

2.182 

13.32 

4 

12.566 

94.00 

7 

38.48 

287.88 

1      9 

2.405 

17.99 

4      1 

13.095 

97.96 

7      3 

41.28 

308.81 

1    10 

2.640 

19.75 

4      2 

13.635 

102.00 

7      6 

44.18 

330.48 

1    11 

2.885 

21.58 

4      3 

14.186 

106.12 

7      9 

47.17 

352.88 

2 

3.142 

23.50 

4      4 

14.748 

110.32 

8 

50.27 

376.01 

2      1 

3.409 

25.50 

4      5 

15.321 

114.61 

8      3 

53.46 

399.88 

2      2 

3.687 

27.58 

4      6 

15.90 

118.97 

8      6 

56.75 

424.48 

2      3 

3.976 

29.74 

4      7 

16.50 

123.42 

8      9 

60.13 

449.82 

2      4 

4.276 

31.99 

4      8 

17.10 

127.95 

9 

•    63.62 

475.89 

2      5 

4.587 

34.31 

4      9 

17.72 

132.56 

9      3 

67.20 

502.70 

2      6 

4.909 

36.72 

4    10 

18.35 

137.25 

9      6 

70.88 

530.24 

2      7 

5.241 

39.21 

4    11 

18.99 

142.02 

9      9 

74.66 

558.51 

2      8 

5.585 

41.78 

5 

19.63 

146.88 

10 

78.54 

587.52 

2      9 

5.940 

44.43 

5      1 

20.29 

151.82 

10      3 

82.52 

617.26  ' 

2    10 

6.305 

47.16 

5 

20.97 

156.83 

10      6 

86.59 

647.74 

2    11 

6.681 

49.98 

5 

21.65 

161.93 

10      9 

90.76 

678.95 

3 

7.069 

52.88 

5 

22.34 

167.12 

11 

95.03 

710.90 

3      1 

7.467 

55.86 

5 

23.04 

172.38 

11      3 

99.40 

743.58 

3      2 

7.876 

58.92 

5 

23.76 

177.72 

11      6 

103.87 

776.99 

3      3 

8.296 

62.06 

5 

24.48 

183.15 

11      9 

108.43 

811.14 

1                                                                   .1 

120                    NATIONAL  TUBE  COMPANY. 

CYLINDRICAL  VESSELS,  TANKS,  CISTERNS,  ETC. 

Diameter  in  Feet  and  Inches,  Area  in  Square  Feet,  and 

U.  S.  Gallons  Capacity  for  One  Foot  in  Depth. 

1  gallon  =  231  cubic  inches  =  0.  1337  cubic  foot. 

(CONTINUED.) 

Diam. 

Area. 

Gals. 

Diam. 

Area. 

Gals. 

Diam. 

Area. 

Gals. 

Ft.  In. 

Sq.ft. 

One  foot 
depth. 

Ft.  In. 

Sq.ft. 

One  foot 
depth. 

Ft.  In. 

Sq.ft. 

One  foot 
depth. 

12 

113.10 

846.03 

19 

283.53 

2120.9 

26 

530.93 

3971.6 

12      3 

117.86 

881.65 

19      3 

291.04 

2177.1 

26      3 

541.19 

4048.4 

12      6 

122.72 

918.00 

19      6 

298.65 

2234.0 

26      6 

551.55 

4125.9 

12      9 

127.68 

955.09 

19      9 

306.35 

2291.7 

26      9 

562.00 

4204.1 

13 

132.73 

992.91 

20 

314.16 

2350.1 

27 

572.56 

4283.0 

13      3 
13      6 

137.89 
143.14 

1031.5 
1070.8 

20      3 
20      6 

322.06 
330.06 

2409.2 
2469.1 

27      3 
27      6 

583.21 
593*96 

4362.7 
4443.1 

13      9 

148.49 

1110.8 

20      9 

338.16 

2529.6 

27      9 

604.81 

4524.3 

14 

153.94 

1151.5 

21 

346.36 

2591.0 

28 

615.75 

4606.2 

14      3 

159.48 

1193.0 

21      3 

354.66 

2653.0 

28     3 

626.80 

4688.8 

14      6 

165.13 

1235.3 

21      6 

363.05 

2715.8 

28      6 

637.94 

4772.1 

14      9 

170.87 

1278.2 

21      9 

371.54 

2779.3 

28     9 

649.18 

4856.2 

15 

176.71 

1321.9 

22 

380.13 

2843.6 

29 

660.52 

4941.0 

15      3 

182.65 

1366.4 

22      3 

388.82 

2908.6 

29      3 

671.96 

5026.6 

15      6 

188.69 

1411.5 

22      6 

397.61 

2974.3 

29      6 

683.49 

5112.9 

15      9 

194.83 

1457.4 

22      9 

406.49 

3040.8 

29      9 

695.13 

5199.9 

16 

201.06 

1504.1 

23 

415.48 

3108.0 

30 

706.86 

5287.7 

16      3 

207.39 

1551.4 

23      3 

424.56 

3175.9 

30      3 

718.69 

5376.2 

16      6 

213.82 

1599.5 

23      6 

433.74 

3244.6 

30      6 

730.62 

5465.4 

16      9 

220.35 

1648.4 

23      9 

443.01 

3314.0 

30      9 

742.64 

5555.4 

17 

226.98 

1697.9 

24 

452.39 

3384.1 

31 

754.77 

5646.1 

17      3 

233.71 

1748.2 

24      3 

461.86 

3455.0 

31      3 

766.99 

5737.5 

17      6 

240.53 

1799.3 

24      6 

471.44 

3526.6 

31      6 

779.31 

5829.7 

17      9 

247.45 

1851.1 

24      9 

481.11 

3598.9 

31      9 

791.73 

5922.6 

18 

254.47 

1903.6 

25 

490.87 

3672.0 

32 

804.25 

6016.2 

18      3 

261.59 

1956.8 

25      3 

500.74 

3745.8 

32      3 

816.86 

6110.6 

18      6 

268.80 

2010.8 

25      6 

510.71 

3820.3 

32      6 

829.58 

6205.7 

18     9 

276.12 

2065.5 

25      9 

520.77 

3895.6 

32      9 

842.39 

6301.5 

;                                                                        •              "       i 

NATIONAL  TUBE  COMPANY.                      121 

Weight  of  Water  in  Foot  Lengths  of  Pipe 

of  Different  Bores. 

(62.425  Lbs.  Per  Cubic  Foot.) 

Bore 

Water 

Bore 

Water 

Bore 

Water 

Bore 

Water 

In. 

Lbs. 

In. 

Lbs. 

In. 

Lbs. 

In. 

Lbs. 

% 

0.0053 

3 

3.0643 

7y 

20.450 

17 

98.397 

k 

0.0213 

31^ 

3.3250 

84 

21.790 

17% 

104.27 

% 

0.0479 

3/4 

3.5963 

8k 

23.174 

18 

110.31 

i/ 

0.0851 

3% 

3.8782 

24.599 

18% 

116.53 

% 

0.1330 

4.1708 

8M 

26.068 

19 

122.91 

% 

0.1915 

35'8 

4.4741 

9 

27.579 

19% 

129.47 

% 

0.2607 

3/iL 

4.7879 

9k 

29.132 

20 

136.19 

i 

0.3405 

3/% 

5.1125 

gi/ 

30.728 

21 

150.15 

\y^ 

0.4309 

4 

5.4476 

9% 

32.366 

22 

164.79 

ik 

0.5320 

4k 

6.1498 

10 

34.048 

23 

180.11 

1% 

0.6437 

6.8946 

10% 

37.537 

24 

196.11 

\TL/ 

0.7661 

4/4 

7.6820 

11 

41  .  198 

25 

212.80 

\% 

0.8997 

5 

8.5119 

11% 

45.028 

26 

230.16 

1% 

1.0427 

5^ 

9.3844 

12 

49.028 

27 

248.21 

\y 

1.1970 

10.299 

12% 

53.199 

28 

266.93 

2 

1.3619 

5% 

11.257 

13 

57.540 

29 

286.34 

2/^5 

1.5375 

6 

12.257 

13% 

62.052 

30 

306.43 

2V 

1.7237 

6k 

13.300 

14 

66.733 

31 

327.20 

2% 

1.9205 

6% 

14.385 

14% 

71.585 

32 

348.65 

2.1280 

6% 

15.513 

15 

76.607 

33 

370.78 

2% 

2.3461 

7 

16.683 

15% 

81.799 

34 

393.59 

2% 

2.5748 

7k 

17.896 

16 

87.162 

35 

417.08 

2.8142 

19.152 

1«« 

92.694 

36 

441.26 

Weights  of  water  in  cylinders  of  the  same  length  are 

proportional  to  the  squares  of  the  diameters.     Therefore, 

to  get  weight  of  cylinder  of  water  one  foot  long  and  60 

inches  diameter,  take  from  above  table  weight  of  water 

of  30  inch  pipe  and  multiply  it  by  the  square  of  60  -f-  30, 

or  the  square  of  two  ;  thus,  306.43  X  4  =  1225.72  =  the 

weight  of  water  in  one  foot  length  of  a  60  inch  pipe. 

*n  _  ^, 

122  NATIONAL  TUBE  COMPANY. 


s 


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eo  1-1  TJ<  as  co  o  «o"  «o  oo  ^  TJH  «o  so  <M_  «o  o« 


sl2SSIIllliEil61§ilSilg 


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s  os  o  m  o  o  jo  io  oi  os  co'  w'  eo  w  os  z>  o  os  <M' 
-  •  -  r  7J  -  '  fc  Sfie  H  5nSS 


:  "     —  -    y^ 
NATIONAL  TUBE  COMPANY.                      123 

Number 

of  U.  S,  Gallons  in  Rectangular  Tanks. 
For  One  Foot  in  Depth. 

£ 

at! 

fl 

LENGTH  OF  TANK  IN  FEET. 

2 

2.5 

3 

3.5 

1 

4.5 

5 

5.5 

6 

6.5 

7 

2 

2.5 
3 
3.5 
4 
4.5 
5 
5.5 
6 
6.5 
7 

29.92S 
4 

7.40 

0.75 

44.88 
50.10 
67.32 

K.4 

78.5 
91.0 

6    59.  * 
5    74.  { 
4    89.' 
4104.' 
.  119.  ( 

J4 

50 

7 
:! 
9 

67.3 
841 
100.9 
117.8 
134.6 
151.41 

J   74.8 
5    93.51 
)  112.21 
2  130.91 
5  149.61 
J  168.31 
187.01 

82.2? 
102.86 
123.42 
144.0C 
164.5? 
185.14 
205.71 
226.28 

89.77 
112.21 
134.65 
157.09 
179.53 
201.97 
224.41 
246.86 
269.30 

97.25 
121.56 
145.87 
170.18 
194.49 
218.80 
243.11 
267.43 
291.74 
316.05 

104.73 
130.91 
157.09 
183.27 
209.45 
235.63 
261.82 
288.00 
314.18 
340.36 
366.54 

Width  in  I 
Feet. 

LENGTH  OF  TANK  IN  FEET. 

7.5 

8 

8.5 

9 

9.5 

10 

10.5 

11 

11.5 

12 

179.53 
224.41 
269.30 
314.18 
359.06 
403.94 
448.83 
493.71 
538.59 
583.47 
628.36 
673.24 
718.12 
763.00 
807.89 
852.77 
897.66 
942.56 
987.43 
1032.3 
1077.2 

2 
2.5 
3 
3.5 
4 
4.5 
5 
5.5 
6 
6.5 
7 
7.5 
8 
8.5 
9 
9.5 
10 
10.5 
11 
11.5 
12 

112.21 
140.26 
168.31 
196.36 
224.41 
252.47 
280.  5£ 
308.5? 
330.  G* 
:50l  C»" 
392.  7S 
420.  76 

119.69 
149.61 
179.53 
209.45 
239.37 
269.30 
299.22 
329.14 
359.06 
388.98 
418.91 
448.83 
478.75 

127.17 
158.96 
190.75 
222.54 
•-.>:>}.:  il 
286.13 
317.92 
349.71 
381.50 
413.30 
445.09 
476.88 
508.67 
540.40 

134.65 
168.31 
202.97 
235.63 
269.30 
302.96 
186.68 
370.28 
103.94 
187.60 
171.27 
504.93 
538.59 
572.26 
505.92 

1-. 

2 

•-' 

•I 

;; 

:;. 

:j< 

(• 

41 

1< 

.V 
5( 
(i( 
6! 
9i 

12.13 
7.66 
3.19 
18.73 
J4.26 
9.79 
5.32 
(0.85 
J6.39 
1.92 
7.45 
2.98 
8.51 
K4.05 
9.58 
5.11 

149.61 
187.01 
224.41 
261.82 
299.22 
336.62 
374.03 
111.43 
148.83 
186.23 
523.64 
561.04 
598.441 
;:  fcVHl 
373.25 
?10.  65 
748.05 

157.09 
196.36 
235.63 
274.90 
314.18 
353.45 
392.72 
432.00 
471.27 
510.54 
549.81 
589.08 
128.86 
>07  C,:{ 
-00.90 
746.17 
?85.45 
324.73 

164.57 
205.71 
246.86 
288.00 
329.14 
370.28 
411.43 
452.57 
493.71 
534.85 
575.99 
617.14 
VS8.S6 
199.42 
740.56 
781.71 
BS8.86 
804.00 
905.14 

172.05 

215.06 
258.07 
301.09 
344.10 
387.11 
430.13 
473.14 
516.15 
559.16 
602.18 
645.19 
688.20 
731.21 
774.23 
817.24 
800.20 
903.26 
946.27 
989.29 

EXAMPLE.  —  To  find  number  of  gallons  in  a  rectangular 
tank  that  is  7.5  ft.  by  10  ft.,  the  water  being  4  ft.  deep  : 
Look  in  extreme  left  hand  column  for  7.5  and  opposite 
to  this  in  column  headed  "  10  "  read  561.04,  which  being 
multiplied  by  4,  the  depth  of  water  in  the  tank,  gives 
2244.2  the  number  of  gallons  required. 

NATIONAL  TUBE  COMPANY. 


.—  Diameters  in  Inches.  (Ellis.) 

given  below,  varying  with  the  form  of  nozzle  or 
d  for  a  good  form  of  tapering  smooth  nozzle 


or  N 

oret 


cal  o 
cent., 


64 


Theoretical  Discharge  of  Circular  Orifi 

OTE.—  The  actual  discharge  will  be  less  than  the  t 
through  which  the  water  flows.  For  a  ring  nozzle 
t  82  per  cent.,  can  be  assumed  as  the  actual  dischar 


In 


NATIONAL  TUBE  COMPANY. 


WATER-POWER. 

(Kent's  Pocket  Book.) 

Power  of  a  Fall  of  "Water—  Efficiency.—  The  gross  power 
of  a  fall  of  water  is  the  product  of  the  weight  of  water 
discharged  in  a  unit  of  time  into  the  total  head,  i.  e.  ,  the 
difference  of  vertical  elevation  of  the  upper  surface  of  the 
water  at  the  points  where  the  fall  in  question  begins  and 
ends.  The  term  "  head  "  used  in  connection  with  water- 
wheels  is  the  difference  in  height  from  the  surface  of  the 
water  .  in  the  wheel-pit  to  the  surface  in  the  pen-stock 
when  the  wheel  is  running. 

If  Q  —  cubic  feet  of  water  discharged  per  second,  D  = 
weight  of  a  cubic  foot  of  water  =  62.36  Ibs.  at  60°  F.,  H 
=  total  head  in  feet  ;  then 

DQH  •=.  gross  power  in  foot-pounds  per  second, 
and  DQH  -f-  550  =  0.1134  QH=  gross  horse  power. 

If  Q'  is  taken  in  cubic  feet  per  minute, 
H.  P.  = 


A  water-wheel  or  motor  of  any  kind  cannot  utilize  the 
whole  of  the  head  H,  since  there  are  losses  of  head  at 
both  the  entrance  to  and  the  exit  from  the  wheel.  There 
are  also  losses  of  energy  due  to  friction  of  the  water  in  its 
passage  through  the  wheel.  The  ratio  of  the  power  de- 
veloped by  the  wheel  to  the  gross  power  of  the  fall  is  the 
efficiency  of  the  wheel.  For  75$  efficiency,  net  horse- 


power =  0.00142g'//= 

706 


NATIONAL  TUBE  COMPANY. 


Horse-power  of  "Water  Flowing  in  a  Tube*  —  The  head  due 

to  the  velocity  is  —  ;  the  head  due  to  the  pressure  is  £-  ; 
2^-'  w* 

the  head  due  to  actual  height  above  the  datum  plane  is  h 

feet.     The  total  head  is  the  sum  of  these  —  —  4-  h  +  £- 

Kg  W 

in  feet,  in  which  v  —  velocity  in  feet  per  second,  f  — 
pressure  in  Ibs.  per  sq.  ft.,  w  =  weight  of  1  cu.  ft.  of 
water  —  62.4  Ibs.  If  p  =  pressure  in  Ibs.  per  sq.  in., 

L  =  2.309/.     In  hydraulic  transmission  the  velocity  and 

the  height  above  datum  are  usually  small  compared  with 
the  pressure-head.  The  work  or  energy  of  a  given  quan- 
tity of  water  under  pressure  =  its  volume  in  cubic  feet  X 
its  pressure  in  Ibs.  per  sq.  ft.;  or  if  Q  =  quantity  in  cubic 
feet  per  second,  and/  =  pressure  in  Ibs.  per  square  inch, 


W=  144/0,  and  the  H.  P.  =  -  0.2618/0. 

550 

Formula  for  Computing  Power  of  Jet  Water-Wheels  of  the 

Pelton  Type.    (F.  K.  Blue). 

Let  HP  =  horse-power  delivered  by  the  water-wheel  ; 
d  =  diameter  of  nozzle  ;  w  =  weight  of  one  cu.  ft.  of 
water,  or  62.5  Ibs.  ;  E  =  efficiency  of  the  water-wheel  ;  q  — 
quantity  of  water  in  cubic  feet  per  minute  ;  c  —  coefficient 
of  discharge  from  the  nozzle,  which  may  be  ordinarily 
taken  as  0.9  ;  li  —  effective  head  (actual  head  less  friction 
head)  in  feet  ;  then 

HP  =  wE^h  =  0.00189  E  q  h  =  0.00436  E  q  p.  = 
33,000 

0.00496  E  c  d2  |/1T»  s=  0.0174  E  c  d2  |/"p"». 
q  =  529  HP  =  2.62  c  d8  V"hT=  4  c  d2  4/~p~». 


NATIONAL  TUBE  COMPANY.  127 

The  Pclton  Water-wheel.— Mr.  Ross  E.  Browne  (En^g 
News,  Feb.  20,  1892)  thus  outlines  the  principles  upon 
which  this  water-wheel  is  constructed  : 

The  function  of  a  water-wheel,  operated  by  a  jet  of 
water  escaping  from  a  nozzle,  is  to  convert  the  energy  of 
the  jet,  due  to  its  velocity,  into  useful  work.  In  order  to 
utilize  this  energy  fully  the  wheel-bucket,  after  catching 
the  jet,  must  bring  it  to  rest  before  discharging  it,  with- 
out inducing  turbulence  or  agitation  of  the  particles. 

This  cannot  be  fully  effected,  and  unavoidable  difficul- 
ties necessitate  the  loss  of  a  portion  of  the  energy.  The 
principal  losses  occur  as  follows  :  First,  in  sharp  or  an- 
gular diversion  of  the  jet  in  entering,  or  in  its  course 
through  the  bucket,  causing  impact,  or  the  conversion  of 
a  portion  of  the  energy  into  heat  instead  of  useful  work. 
Second,  in  the  so-called  frictional  resistance  offered  to 
the  motion  of  the  water  by  the  wetted  surfaces  of  the 
buckets,  causing  also  the  conversion  of  a  portion  of  the 
energy  into  heat  instead  of  useful  work.  Third,  in  the 
velocity  of  the  water,  as  it  leaves  the  bucket,  representing 
energy  which  has  not  been  converted  into  work 

Hence,  in  seeking  a  high  efficiency  :  1.  The  bucket- 
surface  at  the  entrance  should  be  approximately  parallel 
to  the  relative  course  of  the  jet,  and  the  bucket  should 
be  curved  in  such  a  manner  as  to  avoid  sharp  angular  de- 
flection of  the  stream.  If,  for  example,  a  jet  strikes  a 
surface  at  an  angle  and  is  sharply  deflected,  a  portion  of 
the  water  is  backed,  the  smoothness  of  the  stream  is  dis- 
turbed, and  there  results 
considerable  loss  by  im- 
pact and  otherwise.  The 
entrance  and  deflection 
in  the  Pelton  bucket  are 
such  as  to  avoid  these 
losses  in  the  main.  F«>-  134.  FIG.  135. 

2.  The  number  of  buckets  should  be  small,  and  the 
path  of  the  jet  in  the  bucket  short ;  in  other  words,  the 
total  wetted  surface  should  be  small,  as  the  loss  by  fric- 
tion will  be  proportional  to  this. 


128  NATIONAL  TUBE  COMPANY. 

3.  The  discharge  end  of  the  bucket  should  be  as  nearly 
tangential  to  the  wheel  periphery  as  compatible  with 
the  clearance  of  the  bucket  which  follows  ;  and  great 
differences  of  velocity  in  the  parts  of  the  escaping  water 
should  be  avoided.  In  order  to  bring  the  water  to  rest 
at  the  discharge  end  of  the  bucket,  it  is  shown,  mathe- 
matically, that  the  velocity  of  the  bucket  should  be  one 
half  the  velocity  of  the  jet. 

A  bucket,  such  as  shown  in  Fig.  135,  will  cause  the 
heaping  of  more  or  less  dead  or  turbulent  water  at  the 
point  indicated  by  dark  shading.  This  dead  water  is 
subsequently  thrown  from  the  wheel  with  considerable 
velocity,  and  represents  a  large  loss  of  energy.  The  in- 
troduction of  the  wedge  in  the  Pelton  bucket  (see  Fig. 
134)  is  an  efficient  means  of  avoiding  this  loss. 

A  wheel  of  the  form  of  the  Pelton  conforms  closely  in 
construction  to  each  of  these  requirements. 

In  a  test  made  by  the  proprietors  of  the  Idaho  mine, 
near  Grass  Valley,  Cal.,  the  dimensions  and  results  were 
as  follows  :  Main  supply-pipe,  22  in.  diameter,  6900  ft. 
long,  with  the  head  of  386}£  feet  above  centre  of  nozzle. 
The  loss  by  friction  in  the  pipe  was  1.8  ft.,  reducing  the 
effective  head  to  384.7  ft.  The  Pelton  wheel  used  in  the 
test  was  6  ft.  in  diameter  and  the  nozzle  was  1.89  in.  di- 
ameter. The  work  done  was  measured  by  a  Prony  brake, 
and  the  mean  of  13  tests  showed  a  useful  effect  of  87.3$. 


NATIONAL  TUBE  COMPANY. 


FIG.  136. 
Miners'  Inch  Measurements.  (Pelton  Water  Wheel  Co.) 

The  cut,  Fig.  136,  shows  the  form  of  measuring-box 
ordinarily  used,  and  the  following  table  gives  the  dis- 
charge in  cubic  feet  per  minute  of  a  miner's  inch  of 
water,  as  measured  under  the  various  heads  and  different 
lengths  and  heights  of  apertures  used  in  California. 


Length 
of 

Openings  2  Inches  High. 

Openings  4  Inches  High. 

Opening 

Head  to 

Head  to 

Head  to 

Head  to 

Head  to 

Head  to 

in 

Centre 

Centre 

Centre 

Centre, 

Centre, 

Centre, 

inches. 

5  inches. 

6  inches. 

7  inches. 

5  inches. 

6  inches. 

7  inches. 

Cu  ft. 

Cu  ft. 

Cu.  ft. 

Cu.  ft. 

Cu.  ft. 

Cu.  ft. 

4 

1.348 

1.473 

1.589 

1.320 

1.450 

1.570 

6 

1.355 

1.480 

1.596 

1.336 

1.470 

1.595 

8 

1.359 

1.484 

.600 

1.344 

1.481 

1.608 

10 

1.361 

1.485 

.602 

1.349 

1.487 

1.615 

12 

1.363 

1.487 

.604 

1.352 

1.491 

1.620 

14 

.364 

1.488 

.604 

1.354 

1.494 

1.623 

16 

.365 

1.489 

.605 

1.356 

1.496 

1.626 

18 

.365 

1.489 

.606 

1.357 

1.498 

1.628 

20 

.365 

.490 

•606 

1.359 

1.499 

1.630 

22 

.366 

.490 

.607 

1.359 

1.500 

1.631 

24 

.366 

.490 

.607 

1.360 

1.501 

1.632 

26 

.366 

.490 

.607 

1.361 

1.502 

1.633 

28 

.367 

.491 

.607 

1.361 

1.503 

1.634 

30 

.367 

.491 

.608 

1.362 

1.503 

1.635 

40 

.367 

.492 

.608 

1.363 

1.505 

1.637 

50 

.368 

.493 

.609 

1.364 

1.507 

1.639 

60 

.368 

.493 

.609 

1.365 

1.508 

1.640 

70 

.368 

1.493 

.609 

1.365 

1.508 

1.641 

80 

.368 

1.493 

.609 

1.366 

1.509 

1.641 

90 

.369 

1.493 

1.610 

1.366 

1.509 

1.641 

100 

1.369 

1.494 

1.610 

1.366 

1.509 

1.642 

NATIONAL  TUBE  COMPANY. 


PUMPS  AND  PUMPING  ENGINES. 

(Kent's  Pocket  Book.) 

Theoretical  Capacity  of  a  Pump.—  Let  Q  —  cu.  ft.  per 
min.;  G'  =  Anier.  gals,  per  min.  =  7.48050';  d  =  diam.  of 
pump  in  inches  ;  /  =  stroke  in  inches  ;  A7^  =  number  of 
single  strokes  per  min. 

Capacity  in  cu.  ft.  per  min. 

Q  =  *-     —    —  =  0.0004545AW  ; 
4  •  144  •  12 

Capacity  in  gals,  per  min. 


Diameter  required  for  a  given  capacity  per  min. 


If  v  —  piston  speed  in  feet  per  min., 

d  -  13.54  A/&-  -4.95  A/  '— 
r     v  r     v 

If  the  piston  speed  is  100  feet  per  min.  : 

Nl  =  1200,  and  d  =  1.354  i/^T  =  0.495  \f~G\ 

G'  =  4.0&/2  per  min. 

The  actual  capacity  will  be  from  60#  to  95$  of  the  theo- 
retical, according  to  the  tightness  of  the  piston,  valves, 
suction-pipe,  etc. 

Theoretical  Horse-power  required  to  raise  Water  to  a  given 
Height. 

Let  Q  =  cu.  ft.  per  min.;  G'  =  gals,  per  min.;  W  —  wt. 
in  Ibs.;  P—  pressure  in  Ibs.  per  sq.  ft.;  p  =  pressure  in 
Ibs.  per  sq.  in.;  H—  height  of  lift  in  ft.;  W=  62.36<2',  P 
=  144^,  p  =  0.433  H,  H=  2.309/,  G'  =  7.48050'. 

Hp        Q'P        Q'HxmxAZZ^Q'H__     G'H   . 
33,000  33,000  529.2      3958.7  ' 

HP  =    WH  -  g'X62.36x2.309^  _  Q'p   =      G'p 
33,000  33,000  229.2       1714.5  ' 


NATIONAL  TUBE  COMPANY. 


For  the  actual  horse -power  required  an  allowance  must 
be  made  for  the  friction,  slips,  etc.,  of  engine,  pump, 
valves,  and  passages. 

Depth  of  Suction* — Theoretically  a  perfect  pump  will 
lift  water  from  a  depth  of  nearly  34  feet,  corresponding 
to  a  perfect  vacuum  (14.7  Ibs.  X  2.309  =  33.95  feet);  but 
since  a  perfect  vacuum  cannot  be  obtained,  on  account  of 
valve-leakage,  air  contained  in  the  water,  and  the  vapor 
of  the  water  itself,  the  actual  height  is  generally  less 
than  30  feet.  In  pumping  hot  water,  the  water  must  flow 
into  the  pump  by  gravity.  The  following  table  shows 
the  theoretical  maximum  depth  of  suction  for  different 
temperatures,  leakage  not  considered  : 


fi« 

^3    - 

b 

^  2:2--' 

'p^b 

&l   - 

fe 

£«;§-2 

'fl^b 

^1    . 

ex 

QooS 

cx 

J^ftij 

3"o  « 

.  ?£ 

0) 

J^O.^ 

||S  • 

.J3|> 

H 

<|jj| 

^a 

So 

H 

<|^s 

|o 

101.4 

1 

27.88 

31.6 

183.0 

8 

13.63 

15.5 

126.2 

2 

25.85 

29.3 

188.4 

9 

11.59 

13.2 

144.7 

3 

23.81 

27.0 

193.2 

10 

9.55 

10.9 

153.3 

4 

21.77 

24.7 

197.6 

11 

7.51 

8.5 

162.5 

5 

19.74 

22.4 

201.9 

12 

5.48 

6.2 

170.3 

6 

17.70 

20.1 

205.8 

13 

3.44 

3.9 

177.0 

7 

15.66 

17.8 

209.6 

14 

1.40 

1.6 

STEAM 

AND 

STEAM  APPARATUS. 


NATIONAL  TUBE  COMPANY. 


STEAM. 

Under  the  ordinary  atmospheric  pressure  of  14.7  pounds 
per  square  inch,  water  boils  at  212°  Fahr.,  passing  off  as 
steam,  the  temperature  at  which  it  boils  varying  with  a 
variation  in  the  pressure. 

Dry  steam  is  steam  not  containing  any  free  moisture. 
It  may  be  either  saturated  or  superheated. 

Wet  steam  is  steam  containing  free  moisture  in  the  form 
of  spray  or  mist,  and  has  the  same  temperature  as  dry 
saturated  steam  of  the  same  pressure. 

Saturated  steam  is  steam  in  its  normal  state,  that  is, 
steam  whose  temperature  is  that  due  its  pressure;  by 
which  is  meant  steam  at  the  same  temperature  as  that  of 
the  water  from  which  it  was  generated  and  upon  which 
it  rests. 

Superheated  steam  is  steam  at  a  temperature  above  that 
due  to  its  pressure. 

A  British  thermal  unit  is  the  quantity  of  heat  required 
to  raise  one  pound  of  water  at  39°.  1  Fahr.  through  one 
degree  of  temperature. 

The  total  heat  of  the  water  is  the  number  of  British 
thermal  units  needed  to  raise  one  pound  of  water  from 
32°F.  to  the  boiling  point,  under  the  given  pressure. 

The  latent  heat  of  steam  is  the  number  of  British  thermal 
units  required  to  convert  one  pound  of  water,  at  the  boil- 
ing point,  into  steam  of  the  same  temperature. 

The  total  heat  of  saturated  steam  is  the  number  of  heat 
units  required  to  raise  a  pound  of  water  from  32 °F.  to 
the  boiling  point,  at  the  given  pressure,  plus  the  number 
required  to  evaporate  the  water  at  that  temperature. 

The  specific  heat  of  steam  is  the  quantity  of  heat  required 
to  raise  the  temperature  of  one  pound  of  steam  through 
one  degree  of  temperature.  In  British  units  and  near 
the  saturation  temperature  it  equals,  at  constant  pres- 
sure, 0.48. 


NATIONAL  TUBE  COMPANY.  136 

The  specific  gravity  of  steam  at  any  temperature  and 
pressure,  as  compared  with  air  of  same  temperature  and 
pressure,  is  approximately  0.622.  One  cubic  inch  of 
water  evaporated  into  steam  at  212°F.  becomes  1646 
cubic  in.,  that  is,  nearly  one  cu.  ft. 

Water  in  contact  with  saturated  steam  has  the  same 
temperature  as  the  steam  itself.  Water  introduced  into 
superheated  steam  will  be  vaporized  until  the  steam  be- 
comes saturated,  and  its  temperature  becomes  that  due 
its  pressure.  Cold  water,  or  water  at  a  lower  temperature 
than  that  of  the  steam,  introduced  into  saturated  steam, 
will  condense  some  of  it,  thus  lowering  both  the  temper- 
ature and  pressure  of  the  rest  until  the  temperature  again 
equals  that  due  its  pressure. 


136                     NATIONAL  TUBE  COMPANY. 

PROPERTIES  OF  SATURATED  STEAM. 

Sew 

£% 

sS  .^ 

°  u   • 

US"$ 

Bri 

«.S  «  c 

•Sou 

•§l'h 

5?|  • 

•E'l^ 

M| 

*  ^  _o 

leSfa 

Item 

»3ffiffl 

II  *CQ 

|«-S 

!§! 

£ 

ffi'3 

h£ 

^0 

1 

101.99 

70.0 

1043.0 

1113.1 

0.00299 

334.5 

2 

126.27 

94.4 

1026.1 

1120.5 

0.00576 

173.6 

3 

141.62 

109.8 

1015.3 

1125.1 

0.00844 

118.5 

4 

153.09 

121.4 

1007.2 

1128.6 

0.01107 

90.33 

5 

162.34 

130.7 

1000.8 

1131.5 

0.01366 

73.21 

6 

170.14 

138.6 

995.2 

1133  8 

0.01622 

61.65 

7 

176.90 

145.4 

990.5 

1135.9 

0.01874 

53.39 

8 

182.92 

151.5 

986.2 

1137.7 

0.02125 

47.06 

9 

188.33 

156.9 

982.5 

1139.4 

0.02374 

42.12 

10 

193.25 

161.9 

979.0 

1140.9 

0.02621 

38.15 

15 

213.03 

181.8 

965.1 

1146.9 

0.03826 

26.14 

20 

227.95 

196.9 

954.6 

1151.5 

0.05023 

19.91 

25 

240.04 

209.1 

946.0 

1155.1 

0.06199 

16.13 

30 

250.27 

219.4 

938.9 

1158.3 

0.07360 

13.59 

35 

259.19 

228.4 

932.6 

1161.0 

0.08508 

11.75 

40 

267.13 

236.4 

927.0 

1163.4 

0.09644 

10.37 

45 

274.29 

243.6 

922.0 

1165.6 

0.1077 

9.285 

60 

280.85 

250.2 

917.4 

1167.6 

0.1188 

8.418 

55 

286.89 

256.3 

913.1 

1169.4 

0.1299 

7.698 

60 

292.51 

261.9 

909.3 

1171.2 

0.1409 

7.097 

65 

297.77 

267.2 

905.5 

1172.7 

0.1519 

6.583 

70 

302.71 

272.2 

902.1 

1174.3 

0.1628 

6.143 

75 

307.38 

276.9 

898.8 

1175.7 

0.1736 

5.760 

80 

311.80 

281.4 

895.6 

1177.0 

0.1843 

5.426 

85 

316.02 

285.8 

892.5 

1178.3 

0.1951 

5.126 

90 

320.04 

290.0 

889.6 

1179.6 

0.2058 

4.859 

95 

323.89 

294.0 

886.7 

1180.7 

0.2165 

4.619 

100 

327.58 

297.9 

884.0 

1181.9 

0.2271 

4.403 

105 

331.13 

301.6 

881.3 

1182.9 

0.2378 

4.205 

110 

334.56 

305.2 

878.8 

1184.0 

0.2484 

4.026 

115 

337.86 

308.7 

876.3 

1185.0 

0.2589 

3.862 

120 

341.05 

312.0 

874.0 

1186  0 

0.2695 

3.711 

125 

344.13 

315.2 

871.7 

1186.9 

0.2800 

3.571 

130 

347.12 

318.4 

869.4 

1187.8 

0.2904 

3.444 

140 

352.85 

324.4 

865.1 

1189.5 

0.3113 

3.212 

150 

358.26 

330.0 

861.2 

1191.2 

0.3321 

3.011 

160 

363.40 

335.4 

857.4 

1192.8 

0.3530 

2.833 

170 

368.29 

340.5 

853.8 

1194.3 

0.3737 

2.676 

180 

372.97 

345.4 

850.3 

1195.7 

0.3945 

2.535 

190 

377.44 

350.1 

847.0 

1197.1 

0.4153 

2.408 

200 

381.73 

354.6 

843.8 

1198.4 

0.4359 

2.294 

225 

391.79 

365.1 

836.3 

1201.4 

0.4876 

2.051 

250 

400.99 

374.7 

829.5 

1204.2 

0.5393 

1.854 

275 

409.50 

383.6 

823.2 

1206.8 

0.5913 

691 

300 

417.42 

391.9 

817.4 

1209.3 

0.644 

.553 

325 

424.82 

399.6 

811.9 

1211.5 

0.696 

.437 

350 

431.90 

406.9 

806.8 

1213.7 

0.748 

.337 

375 

438.40 

414.2 

801.5 

1215.7 

0.800 

.250 

400 

445.15 

421.4 

796.3 

1217.7 

0.853 

1.172 

500 

466.57 

444.3 

779.9 

1224.2 

1.065 

0.939 

The  absolute  pressures  given  in  column  one  may  be  converted 
into  gauge  pressures  by  subtracting  the  constant  14.7  :    Thus,  115 
Ibs.,  absolute  =  115  —  14.7  =  100.3  Ibs.  gauge.                                             > 

NATIONAL  TUBE  COMPANY.                       137 

FACTORS  OF  EVAPORATION* 

ill 

oTa 

STEAM*  PRESSURE  IN  POUNDS  PER 
SQUARE  INCH,  GAUGE. 

HI 

0. 

5. 

15. 

25. 

35. 

45. 

55. 

65. 

75. 

85. 

Dgrs. 

32 

1.187   1.192 

1.199 

1.204 

1.209 

1.212 

1.216 

1.218 

1.221 

1.223 

35 

1.184   1.189 

1.196 

1.201 

1.206 

1.209 

1.213 

1.215 

1.218 

.220 

40 

1.179 

.184 

1.191 

1.196 

1.201 

1.204 

1.208 

1.219 

1.213 

.215 

45 

1.173 

.178 

1.185 

1.190 

1.195 

1.198 

1.202 

1.204 

1.207 

.209 

50 

1.168 

.173 

1.180 

1.185 

1.190 

1.193 

1.197 

1.199 

1.202 

.204 

55 

1.163 

.168 

1.175 

1.180 

.185 

1.188 

1.192 

1.194 

1.197 

.199 

60 

1.158 

.163 

1.170 

1.175 

.180 

1.183 

1.187 

1.189 

1.192 

.194 

65 

1.153 

.158 

1.165 

1.170 

.175 

1.178 

1.182 

1.184 

1.187 

.189 

70 

1.148 

.153 

1.160 

1.165 

.170 

1.173 

1.177 

1.179 

1.182 

.184 

75 

1.143 

.148 

1.155 

1.160 

.165 

1.168 

1.172 

1.174 

1.177 

.179 

80 

1.137 

.142 

1.149 

1.154 

.159 

1.162 

1.166 

1.168 

1.171 

.173 

85 

1.132 

.137 

1.144 

1.149 

.154 

1.157 

1.161 

1.163 

1.166 

.168 

90 

1.127 

.132 

1.139 

1.144 

.149 

1.152 

1.156 

1.158 

1.161 

.163 

95 

1.122 

.127 

1.134 

1.139 

.144 

1.147 

1.151 

1.153 

1.156 

.158 

100 

1.117 

.122 

1.129 

1.134 

.139 

1.142 

1.146 

1.148 

1.151 

.153 

105 

1.111 

.116 

1.123 

1.128 

.133 

1.136 

1.140 

1.142 

1.145 

.147 

110 

1.106 

.111 

1.118 

1.123 

.128 

1.131 

1.135 

1.137 

1.140 

.142 

115 

1.101 

.106 

1.113 

1.118 

.123 

1.126 

1.130 

1.132 

1.135 

.137 

120 

1.096 

.101 

1.108 

1.113 

.118 

1.121 

1.125 

1.127 

1.130 

.132 

125 

1.091 

.096 

1.103 

1.108 

.113 

1.116 

1.120 

1.122 

1.125 

.127 

130 

1.085 

.090 

1.097 

1.102 

.107 

1.110 

1.114 

1.116 

1.119 

.121 

135 

1.080 

.085 

1.092 

1.097 

.102 

1.105 

1.109 

1.111 

.114 

.116 

140 

1.075 

.080 

1.087 

1.092 

.097 

1.100 

1.104 

1.106 

.109 

.111 

145 

1.070 

.075 

1.082 

1.087 

.092 

1.095 

1.099 

1.101 

.104 

.106 

150 

1.065 

.070 

1.077 

1.082 

.087 

1.090 

1.094 

1.096 

.099 

.101 

155 

1.059 

.064 

1.071 

1.076 

.081 

1.084 

1.088 

1.090 

.094 

.095 

160 

1.054 

.059 

1.066 

1.071 

.076 

1.079 

1.083 

1.085 

.088 

.090 

165 

1.049 

1.054 

1.061 

1.066 

.071 

1.074 

1.078 

1.080 

.083 

.085 

170 

1.044 

1.049 

1.056 

1.061 

.066 

1.069 

1.073 

1.075 

.078 

.080 

175 

1.039 

1.044 

1.051 

1.056 

.061 

1.064 

1.068 

1.070 

.073 

.075 

180 

1.033 

1.038 

1.045 

1.050 

.055 

1.058 

1.062 

1.064 

.067 

.069 

185 

1.028 

1.033 

1.040 

1.045 

.050 

1.053 

1.057 

1.059 

.062 

.064 

190 

1.023 

1.028 

1.035 

1.040 

.045 

1.048 

1.052 

1.054 

.057 

.059 

195 

1.018 

1.023 

1.030 

1.035 

.040 

1.043 

1.047 

1.049 

.052 

.054 

200 

1.013 

1.018 

1.025 

1.030 

1.035 

1.038 

1.042 

1.044 

.047 

1.049 

205 

1.007 

1.012 

1.019 

1.024 

1.029 

1.032 

1.036 

1.038 

1.041 

1.043 

210 

1.002 

1.007 

1.014 

1.019 

1.024 

1.027 

1.031 

1.033 

1.036 

1.038 

212 

1.000 

1.005 

1.012 

1.017 

1.022 

1.025 

1.029 

1.031 

1.084 

1.036 

^  n  r 

138                       NATIONAL  TUBE  COMPANY. 

FACTORS  OF   EVAPORATION. 

ill 

STEAM  PRESSURE  IN  POUNDS  PER 
SQUARE  INCH,  GAUGE. 

<i>^  a 

||| 

95. 

105. 

115. 

125. 

135. 

145. 

155. 

165. 

175. 

185. 

Dgrs. 

32 

1.226 

1.228 

.230 

1.231 

1.233 

1.235 

1.236 

1.238 

1.239 

1.240 

35 

1.223 

1.225 

.227 

1.228 

1.230 

1.232 

1.233 

1.235 

1.236 

1.237 

40 

1.218 

1.220 

.222 

1.223 

1.225 

1.227 

1.228 

1.230 

1.231 

1.232 

45 

1.212 

1.214 

.216 

1.217 

1.219 

1.221 

1.222 

1.224 

1.225 

1  226 

50 

1.207 

1.209 

.211 

1.212 

1.214 

1.216 

1.217 

1.219 

1.220 

1.221 

55 

1.202 

1.204 

.206 

1.207 

1.209 

1.211 

1.212 

1.214 

1.215 

1.216 

60 

1.197 

1.199 

.201 

1.202 

1.204 

1.206 

1.207 

1.209 

1.210 

1.211 

65 

1.192 

1.194 

.196 

1.197 

1.199 

1.201 

1.202 

1.204 

1.205 

1.206 

70 

1.187 

1.189 

.191 

1.192 

1.194 

1.196 

1.197 

1.199 

1.200 

1.201 

75 

1.182 

1.184 

.186 

1.187 

1.189 

1.191 

1.192 

1.194 

1.195 

1.196 

80 

1.176 

1.178 

.180 

1.181 

1.183 

1.185 

1.186 

1.188 

1.189 

1.190 

85 

1.171 

1.173 

.175 

1.176 

1.178 

1.180 

1.181 

1.183 

1.184 

1.185 

90 

1.166 

1.168 

.170 

1.171 

1.173 

1.175 

1.176 

1.178 

1.179 

1.180 

95 

1.161 

1.163 

.165 

1.166 

1.168 

1.170 

1.171 

1.173 

1.174 

1.175 

100 

1.156 

1.158 

.160 

1.161 

1.163 

1.165 

1.166 

1.168 

1.169 

1.170 

105 

1.150 

1.152 

.154 

1.155 

1.157 

1.159 

1.160 

1.162 

1.163 

1.164 

110 

1.145 

1.147 

.149 

1.150 

1.152 

1.154 

1.155 

1.157 

1.158 

1.159 

115 

1.140 

1.142 

1.144 

1.145 

1.147 

1.149 

1.150 

1.152 

1.153 

1.154 

120 

1.135 

1.137 

1.139 

1.140 

1.142 

1.144 

1.145 

1.147 

1.148 

1.149 

125 

1.130 

1.132 

1.134 

1.135 

1.137 

1.139 

1.140 

1.142 

1.143 

1.144 

130 

1.124 

1.126 

1.128 

1.129 

1.131 

1.133 

1.134 

1.136 

1.137 

1.138 

135 

1.119 

1.121 

1.123 

1.124 

1.126 

1.128 

1.129 

1.131 

1.132 

1.133 

140 

1.114 

1.116 

1.118 

1.119 

1.121 

1.123 

1.124 

1.126 

1.127 

1.128 

145 

1.109 

1.111 

1.113 

1.114 

1.116 

1.118 

1.119 

1.121 

1.122 

1.123 

150 

1.104 

1.106 

1.108 

1.109 

1.111 

1.118 

1.114 

1.116 

1.117 

1.118 

155 

1.098 

1.100 

1.102 

1.103 

1.105 

1.107 

1.108 

1.110 

1.111 

1.112 

160 

1.093 

1.095 

1.097 

1.098 

1.100 

1.102 

1.103 

1.105 

1.106 

1.107 

165 

1.088 

1.090 

1.092 

1.093 

1.095 

1.097 

1.098 

1.100 

1.101 

1.102 

170 

1.083 

1.085 

1.087 

1.088 

1.090 

1.092 

1.093 

1.095 

1.096 

1.097 

176 

1  078 

1.080 

1.082 

1.083 

1.085 

1.087 

1.088 

1.090 

1.091 

1.092 

180 

1.072 

1.074 

1.076 

1.077 

1.079 

1.081 

1.082 

1.084 

1.085 

1.086 

185 

1.067 

1.069 

1.071 

1.073 

1.074 

1.076 

1.077 

1.079 

1.080 

1.081 

190 

1.062 

1.064 

.066 

1.067 

1.069 

1.071 

1.072 

1.074 

1.075 

1.076 

195 

1.057 

1.059 

.061 

1.062 

1.064 

1.066 

1.066 

1.069 

1.070 

1.071 

200 

1.052 

1.054 

.056 

1.057 

1.059 

1.061 

1.062 

1.064 

1.065 

1.066 

205 

1.046 

1.048 

.050 

1.051 

1.053 

1.055 

1.056 

1.058 

1.059 

1.060 

210 

1.041 

1.043 

.045 

1.046 

1.048 

1.050 

1.051 

1.053 

1.054 

1.055 

212 

1.039 

1.041 

.043 

1.044 

1.046 

1.048 

1.049 

1.051 

1.052 

1.053 

NATIONAL  TUBE  COMPANY. 


Explanation  of  Table  of  Properties  of  Saturated  Steam: 

The  first  column  shows  the  absolute  pressure  of  steam  as 
it  rises  freely  from  water  of  the  same  temperature,  and  is 
equal  to  14.7  Ibs.  -j-  the  pressure  shown  by  the  steam 
gauge. 

The  second  column  shows  the  temperatures  in  degrees 
Fahrenheit  at  which  water  vaporizes  under  the  pressures 
opposite  in  column  one. 

The  third  column  shows  the  number  of  British  thermal 
units  required  to  raise  one  pound  of  water  from  32°F.  to 
the  boiling  temperatures  opposite  in  column  two. 

The  fourth  column  shows  the  number  of  heat  units 
that  are  absorbed,  or  changed  from  sensible  to  latent  heat, 
when  one  pound  of  water  at  the  boiling  point  changes  to 
steam  of  the  same  temperature. 

The  fifth  column  shows  the  number  of  heat  units  ab- 
sorbed when  one  pound  of  water  at  32°F.  has  its  temper- 
ature raised  to  the  boiling  point  and  is  then  changed  to 
steam  at  constant  pressure  and  temperature.  This  column 
gives  the  total  heat  of  formation  of  steam  from  water  at 
32°F. 

The  sixth  column  shows  the  weights  in  pounds  per 
cubic  ft.  of  saturated  steam  at  the  corresponding  pres- 
sures and  temperatures  given  in  columns  one  and  two. 

The  seventh  column  shows  volumes  in  cubic  ft.  of  one 
pound  of  steam. 

Explanation  of  Table  of  Factors  of  Evaporation :  The  fac- 
tors in  this  table  were  obtained,  for  the  various  feed- 
water  temperatures  and  steam  pressures  given,  by  sub- 
tracting the  heat  above  32°F.  in  one  pound  of  feed-water 
from  the  total  heat  above  32°  in  one  pound  of  steam,  and 
then  dividing  the  remainder  thus  obtained  by  965.7,  the 
latent  heat  of  steam  at  atmospheric  pressure. 


140  NATIONAL  TUBE  COMPANY. 


Example: — Given  the  boiler  pressure  =.  105  Ibs.  per 
square  in.  guage,  and  the  feed-water  temperature  =55°F. ; 
to  find  the  factor  of  evaporation.  Look  in  the  column  or 
steam  pressures  headed  105  and  opposite  to  55  degrees  in 
the  first  column,  read  1.204,  the  factor  required.  It  will 
therefore  require  1.204  times  as  many  heat  units  to  evap- 
orate a  certain  weight  of  water  from  a  feed-water  tem- 
perature of  55°F.  into  steam  under  105  pounds  guage  as 
would  be  required  to  evaporate  the  same  weight  of  water 
from  a  temperature  of  212°F.  into  steam  under  one  at- 
mospheric pressure,  that  is,  from  and  at  2J2°F. 

This  table  is  useful  in  rating  boilers  and  in  preparing 
reports  of  tests. 

FLOW  OF  STEAM  FROM  ORIFICES. 

The  flow  of  steam  from  a  vessel  of  one  pressure  into 
that  of  another  pressure  becomes  greater  the  greater  the 
difference  in  pressure  between  the  two  vessels,  until  the 
lower  is  0.58  the  absolute  pressure  of  the  higher.  Any 
further  reduction  of  the  pressure  in  the  second  vessel, 
even  down  to  a  vacuum,  fails  to  enhance  the  flow  of  the 
steam  between  the  two.  In  flowing  through  the  best 
shaped  nozzle  the  steam  expands  to  the  external  pressure 
and  also  to  the  volume  corresponding  to  this  pressure,  so 
long  as  it  is  not  less  than  58  per  cent,  of  the  internal 
pressure.  For  an  external  pressure  of  58  per  cent,  or 
less,  the  ratio  of  expansion  becomes  constant  and  is 
1.624. 


NATIONAL  TUBE  COMPANY. 


OUTFLOW   OF   STEAM   INTO    THE 
ATMOSPHERE. 


(D.  K.  CLARK.) 


Velocity 

Actual 

Initial 
Pressure. 

External 
Pressure. 

Expan- 
sion in 
nozzle. 

of  out- 
flow at 
constant 

velocity 
of  out- 
flow ex- 

Discharge 

density. 

panded  . 

Lbs.  per 
sq.  in. 

Lbs.  per 
sq.  in. 

Ratio. 

Ft.  per 

Ft.  per 

Lbs.  per 
sq.  in.  per 

absolute. 

absolute. 

sec. 

sec. 

minute. 

25.37 

14.7 

1.624 

863 

1401 

22.81 

30 

14.7 

1.624 

867 

1408 

26.84 

40 

14.7 

1.624 

874 

1419 

35.18 

45 

14.7 

1.624 

877 

1424 

39.78 

50 

14.7 

1.624 

880 

1429 

44.06 

60 

14.7 

1.624 

885 

1437 

52.59 

70 

14.7 

1.624 

889 

1444 

61.07 

75 

14.7 

1.624 

891 

1447 

65.30 

90 

14.7 

1.624 

895 

1454 

77.94 

100 

14.7 

1.624 

898 

1459 

86.34 

115 

14.7 

1.624 

902 

1466 

98.76 

135 

14.7 

1.624 

906 

1472 

115.61 

155 

14.7 

1.624 

910 

1478 

132.21 

165 

14.7 

1.624 

912 

1481 

140.46 

215 

14.7 

1.624 

919 

1493 

181.58 

The  weight  of  steam  discharged  from  a  cylindrical 
nozzle  or  a  short  pipe  may  be  approximately  found,  when 
the  pressure  of  the  atmosphere  receiving  the  steam  is 
less  than  58  per  cent,  of  the  initial  pressure,  by  the  fol- 
lowing formula  (Napier's  Rule):  W—ap-r-^\  in  which 
W—  flow  in  pounds  per  second,  a  =  area  of  orifice  in  square 
inches;  and  p  =  absolute  initial  pressure  per  square  inch 
of  the  steam. 

For  a  circular  opening  in  a  thin  pla'te  multiply  the  dis- 
charge as  obtained  from  the  above  formula  by  0.65. 


NATIONAL  TUBE  COMPANY. 


FLOW  OF  STEAM  IN  PIPES. 

(KENT'S  POCKET  BOOK). 

A  formula  commonly  used  for  velocity  of  flow  of  steam 
in  pipes  is  the  same  as  Downing's  for  the  flow  of  water 
in  smooth  cast  iron  pipes,  viz.  : 


V=  604/5  D, 

'      L 

in  which  V—  velocity  in  feet  per  second,  Z,=  length,  and 
D  =  diameter  of  pipe  in  feet,  //'—height  in  feet  of  a  col- 
umn of  steam,  of  the  pressure  of  the  steam  at  the  en- 
trance, which  would  produce  a  pressure  equal  to  the 
difference  of  pressures  at  the  two  ends  of  the  pipe.  (For 
derivation  of  the  coefficient  50,  see  Briggs  on  "  Warming 
Buildings  by  Steam,"  Proc.  Inst.  C.  E.,  1882.) 

If  Q  —  quantity  in  cubic  ft.  per  minute,  d  =  diameter 
in  inches,  L  and  //being  in  feet,  the  formula  reduces  to 

Q  =4.723  \/^ d>5      H=0.448  ~^>    d  =0.537  \/^' 

If  P!  =  pressure  in  pounds  per  sq.  in.  of  the  steam  at 
the  entrance  to  the  pipe,  p2  =  the  pressure  at  the  exit, 
then  144  (p\—p*)  —  difference  in  pressure  per  sq.  ft.  Let 
w  —  density  or  weight  per  cu.  ft.  of  steam  at  the  pressure 
plt  then  the  height  of  column  equivalent  to  the  difference 
in  pressures  is 


If  W=  weight  of  steam  flowing  in  pounds  per  minute 
—  Qw  and  d  is  taken  in  inches,  L  being  in  feet: 

W  =  56.68  |/jy  (Pi-Pa)  d5  ;  Q=  56.68  |/S*~P">  d<  . 
d  =  0.199  !/ — W*  L    .  =  0.199 


Pi— Pa 

d8 
Velocity    in    feet    per    minute  —  V  =  Qn-0.7854    ^ 

=  10390  J  pt  ~p£}  d' 

™ ; j) 


NATIONAL  TUBE  COMPANY. 


For  a  velocity  of  6000  feet  per  minute,  d= 


For  a  velocity  of  6000  feet  per  minute,  a  steam  pressure 
of  100  pounds  gauge,  or  W=0.264,  and  a  length  of  100 
feet. 


Pi—  Pa  d 

That  is,  a  pipe  1  inch  diameter,  100  feet  long,  carrying 
steam  of  100  pounds  gauge  pressure  at  6000  feet  velocity 
per  minute,  would  have  a  loss  of  pressure  of  8.8  pounds 
per  sq.  inch,  while  steam  traveling  at  the  same  velocity 
in  a  pipe  8.8  inches  diameter  would  lose  only  1  pound 
pressure. 

G.  H.  Babcock  in  "Steam,"  gives  the  formula 


)  w  (Pi— p8)  d6 
W=87|/L  /I  +  3.6  \ 


One  of  the  most  widely  accepted  formulae  for  flow  of 
water  is  D'Arcy's,  which  is 

Using  D'Arcy's  coefficients,  and  modifying  his  formula 
to  make  it  apply  to  steam,  to  the  form 


a  =  c  i or  w  =  c  j .-. 

we  obtain  for, 

Diam.  in.  1  2  3  456  78 

Value  of  c,  45.3  52.7  56.1  57.8  58.4  59.5  60.1  60.7 

Diam.  in.  9  10  12  14  16  18  20  24 

Value  of  c,  61.2  61.8  62.1  62.3  62.6  62.7  62.9  63.2 

In  the  absence  of  direct  experiments  these  coefficients 
are  probably  as  accurate  as  any  that  may  be  derived  from 
formulae  for  flow  of  water. 

Loss  of  pressure  in  Ibs.  per  sq.  in.=pl — ps=  Q    w  **  . 

c3  d6 


NATIONAL  TUBE  COMPANY. 


RESISTANCE  TO  FLOW  BY  BENDS, 
VALVES,  ETC 

Mr.  Briggs  states  that  in  "  Warming  Buildings  by 
Steam,"  that  the  resistance  at  the  entrance  to  a  pipe  con- 
sists of  two  parts,  namely:  the  head  ^— ,  which  is  neces- 
sary to  create  the  velocity  of  flow,  and  the  head 

v* 
0.505  -«— »  which  overcomes  the  resistance  to  entrance 

*K 
offered  by  the  mouth  of  the  pipe*    The  total  loss  of  head 

at  entrance  then  equals  the  sum  of  these,  or  1.505-^—, 
in  which  V—  velocity  of  flow  of  steam  in  the  pipe,  in 
feet  per  second,  and  g  =  acceleration  due  to  gravity,  or 
32.2. 

The  Babcock  &  Wilcox  Co.  state  in  "  Steam  "  that  the 
resistance  at  the  opening,  and  that  at  a  globe  valve,  are 
each  about  the  same  as  that  caused  by  an  additional 

length  of  straight  pipe,  as  computed  by  the  formula, 

r      .          114  X  diameter  of  pipe 
Additional  length  of  pipe  =    t  +  (3.6  ^  diametPer^   - 

from  which  has  been  computed  the  following  table: 

Diameter  in  inches  2    2*     3       3|    4      5      6      7 

Additional  length,  feet       7    10    13    16    20    28    36    44 

Diameter  in  inches  8  10  12  15  18  20  22  24 

Additional  length,  feet  53  70  88  115  143  162  181  200 

The  resistance  to  flow  at  a  right-angled  elbow  is  about 
equal  to  %  that  of  a  globe  valve. 

The  above  values  are  to  be  considered  as  being  only 
approximations  to  the  truth. 


NATIONAL  TUBE  COMPANY. 


Example.  —  Find  the  discharge  from  a  steam  pipe  when 
the  given  length  =  120  feet  and  the  diameter  =  8  inches; 
the  pipe  containing  6  right-angled  elbows  and  two  globe 
valves,  the  pressure  at  the  two  ends  being  respectively 

105  and  103  Ibs.  per  sq.  in.  gauge. 

The  resistance  to  entrance,  from  the  above  table,  for  8 
inch  pipe  =  53  feet;  the  resistance  of  6  elbows  =  6  X  53  X  % 
=  212  feet;  the  resistance  of  two  globe  valves  =  2  X  53  = 

106  feet;  making  a  total  resistance=53-{-212  +  106  =  371 
feet  of  additional  length  of  pipe.  Therefore,  the  steam 
would  encounter  the  same  resistance  flowing  through  a 
straight  8-inch  pipe,  whose  length  equals  120  -f-  371,  or 
491  feet,  as  it  would  in  flowing  through  the  given  pipe 
with  its  various  resistances. 


Then  in  the  formula  W 


=  0/1 


i—  P») 


L  =  491  feet;  p^  =  105  Ibs.  per  sq.  in.;  p%  =  103  Ibs.  per 
sq.  in.  ;  d  —  8  inches;  £,  for  an  8-inch  pipe  =  60.7;  and  w, 
from  table  of  Properties  of  Saturated  Steam,  =  0.27 
Substituting  in  formula  we  get 


W  =  60.7  ,/ 0.27  (105-103)8?  =  m 

r  491 

The  pipe,  then,  under  the  stated  conditions,  would  dis- 
charge approximately  364  pounds  of  steam  per  minute, 
or  21,800  Ibs.  per  hour;  which,  on  the  basis  of  30  Ibs. 
per  horse-power  hour,  would  have  a  capacity  of  728 
boiler  horse-power.  Since  one  pound  of  steam  at  104  Ibs. 
gauge  has  a  volume  of  3.7  cu.  ft.,  the  pipe  would  dis- 
charge 1,350  cu.ft.  per  minute,  or  81,000  cu.  ft.  per  hour. 


NATIONAL  TUBE  COMPANY 


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NATIONAL  TUBE  COMPANY. 


The  above  table  was  calculated  by  the  formula  W  OC 

ds 

(varies  as)  ^77g-g-»  in  which  W=  weight  of  fluid  de- 
livered in  a  given  time,  and  d  =  diameter  (internal)  in 
inches.  In  the  upper  right  hand  triangle  of  the  table 
the  figures  refer  to  nominal  diameters,  while  in  the 
lower  triangle  they  refer  to  actual  diameters. 

Example* — To  find  number  of  standard  2  inch  pipes  to 
deliver  as  much  fluid  as  one  standard  1  inch  pipe:  In 
the  upper  triangle  look  in  column  headed  7  and  opposite 
2  in  the  extreme  right  hand  column,  read  29.  Twenty- 
nine  2-inch  pipes  will  then  deliver  as  much  as  one  7-inch 
pipe. 

NON-CONDUCTING  COVERINGS  FOR 
STEAM  PIPES. 

A  bare  pipe  carrying  steam,  and  made  of  iron,  steel  or 
other  conducting  material,  loses  heat  by  convection  to 
the  surrounding  air  and  by  radiation  to  the  surrounding 
objects,  both  of  which  cause  a  loss  of  steam  by  conden- 
sation. 

This  loss  is  lessened  in  practice  by  covering  the  outer 
surface  of  the  steam  pipe  with  a  material  that  will  offer 
a  greater  resistance  to  the  flow  of  heat  than  that  offered 
by  the  material  of  the  pipe. 

A  good  material  for  this  purpose  should  not  suffer  ser- 
ious deterioration  from  the  heat  or  vibration  to  which  it 
would  be  subjected  in  practice;  and  in  all  cases  where 
damage  from  fire  might  result,  it  should  never  consist  of 
combustible  matter.  Under  the  conditions  of  practice, 
especially  in  places  where  it  may  become  damp,  a  good 
pipe  covering  should  consist  of  materials  that  will  not 
rapidly  deteriorate,  and  should  contain  nothing  that  will 
seriously  corrode  the  pipe. 

Since  air  does  not  take  up  heat  by  radiation,  but  re- 
ceives heat  by  contact  with  a  hot  body  only,  it  would  ap- 
pear that  the  greater  the  porosity  of  a  material,  that  is, 
the  greater  the  percentage  of  volume  of  finely  divided 


NATIONAL  TUBE  COMPANY. 


air  it  contains,  the  greater  will  be  its  non-conducting 
qualities.  This  is  noticeably  the  case  in  the  commercial 
pipe  coverings  that  consist  substantially  of  the  same  ma- 
terials, when  these  materials  contain  different  percent- 
ages of  still  air.  In  every  case  the  more  porous  the  ma- 
terial, other  things  being  equal,  the  greater  will  be  its 
non-conducting  properties. 

The  following  table  contains  averages  made  up  from 
results  obtained  by  a  number  of  carefully  conducted 
tests,  and  represent  approximately  what  may  be  ex- 
pected when  these  materials  are  properly  applied  as 
steam-pipe  coverings  in  practice.  The  table  gives  the 
quantity  of  heat  transmitted  through  covered  steam- 
pipes,  when  that  transmitted  through  a  naked  pipe  is 
taken  as  100,  the  covering,  except  where  otherwise  indi- 
cated, being  one  inch  thick. 

Relative  Amount  of 
Kind  of  Covering.  Heat  Transmitted. 

Naked  pipe 100 

Hair  felt,  asbestos  lined  and  canvas  covered. . .  .16  to  18 
Wool  felt,  "  "  "  "  "  ....20  to  22 

Two  layers  of  asbestos  paper 70  to  80 

Four     "       "        "  "      45  to  55 

Asbestos  mixed  with  some  plaster  of  paris 28  to  34 

Magnesia  mixed  with  a  little  asbestos  fiber,  can- 
vas covered 18  to  20 

Best  mineral  wool,  lined  and  canvas  covered 18  to  20 

Pipe  painted  with  black  asphaltum about  105 

Pipe  painted  with  white  glossy  paint "        95 


For  coverings  having  values  less  than  25  in  the  above 
table,  the  values  for  thicknesses  of  covering  of  1*4  and  2 
inches  (those  in  the  table  being  for  one  inch,  as  noted) 
may  be  approximately  obtained  by  multiplying  respec- 
tively by  0.78  and  0.58.  Thus,  a  pipe  covered  with 
magnesia  and  canvas  covered  would  transmit  an  amount, 
if  1  yz  inches  thick  =  (18  to  20)  X  0.78  =  14  to  15.5;  and  if 
2  inches  thick  an  amount  =  (18  to  20)  X  0.58  =  10.5  to 
11.5,  that  transmitted  by  a  similar  bare  pipe  being  100 
in  the  same  length  of  time. 


ar                                                           c 

NATIONAL  TUBE  COMPANY.                     149 

LOSS  OF  HEAT  FROM  BARE  IRON  STEAM  PIPES. 

Steam  pressure=100  Ibs.  gauge,  surrounding  air  at  62°  F. 

Steam  temperature  =  338°  Fahr. 

& 

-55    5 

S, 

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& 

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423 

6 

1221 

12 

2290 

22 

3949 

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494 

7 

1420 

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2645 

24 

4264 

3 

692 

8 

1580 

16 

2961 

26 

4617 

4 

869 

9 

1738 

18 

3315 

28 

4932 

5 

1067 

10 

1935 

20 

3632' 

30 

5288 

CONDENSATION  OF  STEAM  IN  BARE  IRON  PIPES. 

Steam  pressure—  100  Ibs.  gauge,  surrounding  air  at  62°  F. 

Steam  temperature  =  338°  Fahr. 

1*1 

3&J 

Condensed 
.  per  Hour 
ot  Length. 

3minal 
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inches. 

Condensed 
.  per  Hour 
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ominal 
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24 

4.87 

3 

0.79 

8 

1.80 

16 

3.38 

26 

5.27 

4 

0.99 

9 

1.98 

18 

3.78 

28 

5.63 

5 

1.22 

10 

2.21 

20 

4.15 

30 

6.04 

i  n                                                                          . 

NATIONAL  TUBE  COMPANY. 


CONDENSATION   OF   STEAM   IN   COVERED 
IRON   PIPES. 

Corresponding  to  a  percentage  of  that  in  a  bare  pipe 
varying  from  15  per  cent,  for  a  30-inch  pipe  to  19  for  a 
1%  inch  pipe,  which  approximates  to  what  may  be  ex- 
pected in  practice  from  the  application  of  the  best  com- 
mercial pipe  coverings. 

Steam  pressure =100  Ibs.  gauge,  surrounding  air  at  62°  F. 
Steam  temperature  =  338°  Fahr. 


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0.30 

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0.57 

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0.19 

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0.34 

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0.63 

30 

0.90 

Example. — Find  the  saving  resulting  from  covering  an 
8-inch  steam  pipe  that  is  120  feet  long. 
Condensation  in  bare  pipe  =  1.80x120  =  216.0  Ibs.  per  hr. 
"covered"    =0.28x120=33.6    "      "    " 


Saving  of  steam  effected  by  covering  =  182.4  "  "  ' 
Which  on  a  10-hour  basis  would  amount  to  an  annual 
saving  of  about  550,000  pounds  of  steam.  Assuming 
that  one  Ib.  of  coal  evaporates,  under  actual  conditions, 
9  Ibs.  of  water,  the  saving  of  fuel  in  this  case  resulting 
from  the  application  of  a  good  commercial  pipe  covering, 
would  amount  to  about  60,000  Ibs.  of  coal,  or  30  short 
tons  per  annum.  At  two,  three  and  four  dollars  per  ton 
for  fuel  this  would  amount  to  an  annual  saving  of  |60.00, 
$90.00  and  $120.00  respectively. 


NATIONAL  TUBE  COMPANY. 


Since  the  steam  carrying  capacity  of  a  pipe  of  this 
size,  as  ordinarily  installed  for  power  purposes,  would  be 
about  24,000  Ibs.  of  steam  per  hour,  the  above  saving 
would  represent  about  %  of  one  per  cent,  of  its  carrying 
capacity. 

Where  fuel  is  inexpensive  and  the  steam  pipes  are 
short,  the  net  saving  due  to  covering  the  pipes  is,  of 
course,  insignificant;  but  even  in  this  case,  especially  in 
confined  situations,  the  pipes  should  be  ordinarily  cov- 
ered in  order  to  make  the  temperature  of  the  space  near 
them  less  unendurable  to  workmen  and  others,  in  warm 
weather. 


POWER  OF  ENGINES  AND  BOILERS. 

"Work,  in  the  mechanical  sense,  is  the  overcoming  of 
resistance  through  space,  and  is  measured  by  the  amount 
of  the  resistance  multiplied  by  the  distance  through 
which  it  is  overcome. 

The  unit  of  work,  in  Great  Britain  and  the  United 
States,  is  the  foot-pound,  which  is  an  amount  of  energy 
equivalent  to  the  lifting  of  one  pound  through  a  height 
of  one  foot. 

The  unit  of  rate  of  doing  work  is  a  quantity  of  work 
equivalent  to  the  doing  of  33,000  foot-pounds  in  one  min- 
ute, and  is  called  a  horse-power.  This  is  a  mechanical 
horse-power,  and  should  not  be  confused  with  the  boiler 
horse-power,  which  is  based  upon  the  evaporation  of  a 
stated  quantity  of  water  under  certain  stated  conditions. 

The  indicated  horse-power  of  a  steam  engine  is  the 
horse-power  developed  by  the  steam  in  the  cylinder  and 
delivered  to  the  piston.  In  a  double  acting  single  cylin- 

plan 
der  engine,  the  indicated  horse-power  =  gg  QQQ  >  in  which 

^  =  the  mean  effective  pressure  in  Ibs.  per  sq.  in.,  as  ob- 
tained from  the  indicator  card,  /  —  length  of  stroke  in 
feet,  a  — area  of  piston  in  sq.  inches  and  n  —  number  of 
working  strokes  per  minute.  If  the  engine  has  more 
than  one  cylinder  compute  the  power  of  each  and  take 


NATIONAL  TUBE  COMPANY. 


the  sum.  If  great  accuracy  is  desired  the  area  of  cross- 
section  of  piston  rod  should  be  deducted  from  the  piston 
area  for  the  crank  end,  and  the  powers  of  the  two  ends 
computed  separately,  since  the  mean  effective  pressures 
of  the  two  ends  will  not  ordinarily  be  found  to  be  exactly 
the  same.  For  single  acting  engines  substitute  for  n 
the  number  of  working  strokes  only. 

Net  or  brake  horse-power  of  an  engine  is  the  horse- 
power delivered  by  the  engine  from  its  shaft,  by  belt  or 
otherwise.  It  may  be  obtained  from  the  indicated  horse- 
power by  multiplying  by  the  mechanical  efficiency:  For 
example,  an  engine  indicating  300  H.P.,  with  a  mechan- 
ical efficiency  of  88  per  cent.,  would  have  a  net  or  brake 
horse-power  =  300  X  0.88  =  264. 

The  unit  of  evaporation  is  the  number  of  B.T.U.  neces- 
sary to  convert  one  pound  of  water  at  212°F.  into  steam 
of  the  same  temperature,  and  is  therefore  equal  to  965.7 
B.T.U. ,  the  latent  heat  of  one  pound  of  steam  at  atmos- 
pheric pressure. 

Boiler  Horse-power.  A  Committee  of  the  American  So- 
ciety of  Mechanical  Engineers  recommended  the  unit  of 
boiler  power  known  as  the  "Centennial  Standard, "  and 
this  is  now  generally  accepted.  They  advised  that  the 
commercial  horse-power  be  taken  as  an  evaporation  of  30 
pounds  of  water  per  hour  from  a  feed  water  temperature 
of  100°Fahr.  into  steam  at  70  pounds  per  square  inch 
gauge  pressure.  This  is  equivalent  to  34}£  units  of 
evaporation,  that  is,  to  34^  pounds  of  water  evaporated 
from  a  feed  water  temperature  of  212°  Fahr.  into  steam 
at  the  same  temperature.  This  "Centennial  Standard  " 
unit  is  equivalent  to  33,305  British  thermal  units  per  hour. 

It  was  the  opinion  of  this  Committee  that  a  boiler 
rated  at  any  stated  power  should  be  capable  of  developing 
that  power  with  easy  firing,  moderate  draught,  and  ordi- 
nary fuel,  while  exhibiting  good  economy;  and,  at  times, 
when  maximum  economy  is  not  the  most  important  ob- 
ject to  be  attained,  at  least  one-third  more  than  its  rated 
power  to  meet  emergencies. 


NATIONAL  TUBE  COMPANY. 


Example. — A  battery  of  boilers  evaporate  20,000  Ibs.  of 
feed- water  per  hour,  the  temperature  of  feed-water  beijig 
40°F.,  and  the  gauge  pressure  100  Ibs.  per  sq.  in.  Find 
the  equivalent  evaporation  from  and  at  2J2°F.j  also  the 
commercial  horse-power. 

The  factor  of  evaporation,  from  4O°F.  and  at  100  Ibs. 
gauge,  is  (see  table  of  factors  of  evaporation)  1.219. 
Therefore  the  equivalent  evaporation  from  and  at  212°  = 
20,000  X  1.219  =  24,380  Ibs.  per  hr. 

Since  one  commercial  horse-power  is  equivalent  to  the 
evaporation  of  34.5  Ibs.  of  water  per  hour,  from  and  at 
212°,  the  commercial  horse-power  =  24,380-5-34.5  =  707. 

In  the  above  example  the  steam  is  assumed  to  be  dry 
and  saturated.  In  case  it  is  not  a  correction  must  be 
made. 

1.  Assume  that  the  steam  contains  2  per  cent,  of  mois- 
ture.    Of  the  20,000  Ibs.  of  feed-water,  then,  98  per  cent, 
or  19,600  Ibs.  will  be  evaporated  and  the  remaining  400 
Ibs.  will  pass  from  the  boiler  as  water  at  the  temperature 
of  the  steam.     Each  pound  of  this  water  will  carry  away 
from  the  boiler  an  amount  of  heat  necessary  to  raise  its 
temperature  from  40°F.,  the  temperature  of  the  feed- 
water,  to  337°,  the  temperature  of  the  steam,  or  296  B.T.U. 
per  Ib.  of  entrained  water.     Had  the  entrained   water 
been  evaporated  each  pound  would  have  carried  away  an 
additional  amount  equal  to  its  latent  heat  at  boiler  pres- 
sure, or  876  B.T.U.  per  Ib.,  or  876  X  400  =  350,400  B.T.U. 
per  hour,  for  the  total  amount  of  entrained  water.     Un- 
der the  assumed  conditions,  then,  the  boiler  imparts 
350,400  heat  units  less  to  the  feed-water  per  hour  than 
would  have  been  the  case  had  there  been  no  entrained 
water;  that  is,  its  capacity  is  less  by  350,400-^33,305  (the 
heat  equivalent  of  a  boiler  H.P.)  =  10.5  horse-power.    The 
actual  commercial  horse-power  of  the  boiler  then  =707  — 
10.5  =  696.5. 

2.  Assume  that  the  steam  is  superheated  20  degrees; 
that  is,  to  a  temperature  of  337°  -f  20°  =  357°  F.    Then  the 
additional  heat  imparted  to   each  pound  of  feed- water 
over  that  necessary  to  generate  dry  saturated  steam  is 
20°  X  0.48  (the  specific  heat  of  steam)  =  9.6  heat  units  per 
Ib.,  or  9.6  X  20,000  =  192,000  per  hr.,  or  192.000-^-33,305  = 
5.8  horse-power.     The  actual  horse-power  of  boiler  then 
=  707  +  5.8  =  712.8. 


x-ri  ,  —  p^ 

154                      NATIONAL  TUBE  COMPANY. 

Horse-power  per  Pound  Mean  Effective  Pressure* 

T?nrtnii1*      Ar6a  in  SC3-   in-    X  piston-Speed 

33,000 

«•£ 

SPEED  OF  PISTON  IN  FEET  PER  MINUTE. 

J>  »., 

6* 

rt^- 
.c 
">, 

100 

200 

300 

400 

500 

600 

700 

800 

900 

u 

4 

.0381 

.0762 

.1142 

.1523 

.1904 

.2285 

.2666 

.3046 

"73427 

4V< 

.0482 

.0964 

.1446 

.1928 

.2410 

.2892 

.3374 

.3856 

.4338 

5 

.0595 

.1190 

.1785 

.2380 

.2975 

.3570 

.4165 

.4760 

.5355 

5V( 

.0720 

.1440 

.2160 

.2880 

.3600 

.4320 

.5040 

.5760 

.6480 

6 

.0857 

.1714 

.2570 

.3427 

.4284 

.5141 

.5998 

.6854 

.7711 

.1006 

.2011 

.3017 

.4022 

.5028 

.6033 

.7039 

.8044 

.9050 

7 

.1166 

.233-2 

.3499 

.4665 

.5831 

.6997 

.8163 

.9330 

1.0496 

.1339 

.2678 

.4016 

.5355 

.6694 

.8033 

.9371 

1.0710 

1.2049 

8 

.1523 

.3046 

.4570 

.6093 

.7616 

.9139 

1.0662 

1.2186 

1.3709 

.1720 

.3439 

.5159 

.6878 

.8598 

.0317 

1.2037 

1.3756 

1.5476 

9 

.1928 

.3856 

.5783 

.7711 

.9639 

.1567 

1.3495 

1.5422 

1.7350 

.2148 

.4296 

.6444 

.8592 

1.0740 

.2888 

1.5036 

1.7184 

1.9532 

10 

.2380 

.4760 

.7140 

.9520 

1.1900 

.4280 

1.6660 

1.9040 

2.1420 

11 

.2880 

.5760 

.8639 

1.1519 

1.4399 

.7279 

2.0159 

2.3038 

2.5818 

12 

.3427 

.6854 

1.0282 

1.3709 

1.7136 

2.0563 

2.3990 

2.7418 

3.0845 

13 

.4022 

.8044 

1.2067 

1.6089 

2.0111 

2.4133 

2.8155 

3.2178 

3.6200 

14 

.4665 

.9330 

1  3994 

1  8659 

2  3324 

9,  7989 

3  2654 

3.7318 

4  1983 

15 

.5355 

1.0710 

1.6065 

2.1420 

2.6775 

3.2130 

3.7485 

4.2840 

4.8195 

16 

.6093 

1.2186 

1.8278 

2.4371 

3.0464 

3.6557 

4.2650 

4.8742 

5.4835 

17 

.6878 

1.2756 

1.9635 

2.6513 

3.3391 

4.0269 

4.6147 

5.4026 

6.1904 

18 

.7711 

1.5422 

2.3134 

3.0845 

3.8556 

4.6267 

5.3978 

6.1690 

6.9401 

19 

.8592 

1.7184 

2.5775 

3.4367 

4.2959 

5.1551 

6.0143 

6.8734 

7.7326 

20 

.9520 

1.9040 

2.8560 

3.8080 

4.7600 

5.7120 

6.6640 

7.6160 

8.5680 

21 

1.0496 

2.0992 

3.1488 

4.1983 

5.2479 

6.2975 

7.3471 

8.3966 

9.4462 

22 

1.1519 

2.3038 

3.4558 

4.6077 

5.7596 

6.9115 

8.0634 

9.2154 

10.367 

23 

1.2590 

2.5180 

3.7771 

5.0361 

6.2951 

7.5541 

8.8131 

10.072 

11.331 

24 

1.3709 

2.7418 

4.1126 

5.4835 

6.8544 

8.2253 

9.5962 

10.967 

12.338 

25 

1.4875 

2.9750 

4.4625 

5.9500 

7.4375 

8.9250 

10.413 

11.900 

13.388 

26 

1.6089 

3.2178 

4.8266 

6.4355 

8.0444 

9.6534 

11.262 

12.871 

14.480 

27 

1.7350 

3.4700 

5.2051 

6.9401 

8.6751 

10.410 

12.145 

13.880 

15.615 

28 

1.8659 

3.7318 

5.5978 

7.4637 

9.3296 

11.196 

13.061 

14.927 

16.793 

29 

2.0016 

4.0032 

6.0047 

8.0063 

10.008 

12.009 

14.011 

16.013 

18.014 

30 

2.1420 

4.2840 

6.4260 

8.5680 

10.710 

12.852 

14.994 

17.130 

19.278 

32 

-i.4371 

4.8742 

7.3114 

9.7485 

12.186 

14.623 

17.060 

14.497 

21.934 

34 

2.7513 

6.5026 

8.2538 

1.005 

13.756 

16.508 

19.259 

22.010 

24.762 

36 

3.0845 

6.1690 

9.2534 

12.338 

15.422 

18.507 

21.591 

24.676 

27.760 

38 

3.4367 

6.8734 

10.310 

13.747 

17.184 

20.620 

24.057 

27.494 

30.930 

40 

3.8080 

7.6160 

11.424 

15.232 

9.040 

22.848 

26.656 

30.464 

34.272 

42 

4.1983 

8.3866 

12.585 

16.783 

20.982 

25.180 

29.378 

33.577 

37.775 

44 

4.6077 

9.2154 

3.823 

8.431 

23.038 

27.646 

32.254 

36.861 

41.469 

46 

5.0361 

0.072 

5.108 

20.144 

25.180 

30.216 

35.253 

40.289 

45.325 

48 

5.4835 

0.967 

6.451 

21.934 

27.418 

32.901 

38.385 

43.868 

49.352 

50 

5.9500 

1.900 

7.850 

23.800 

29.750 

35.700 

41.650 

47.600 

53.550 

52 

6.4355 

2.871 

9.307 

25.742 

32.178 

38.613 

45.049 

51.484 

57.920 

54 

6.9401 

3.880 

20.820 

27.760 

34.700 

41.640 

48.581 

55.521 

62.461 

56 

7.4637 

4.927 

22.391 

29.855 

37.318 

44.782 

52.246 

59.709 

67.173 

58 

8.0063 

6.013 

24.019 

32.025 

0.032 

48.038 

56.044 

64.051 

72.057 

60 

8.5680 

7.136 

25.704 

34.272 

42.840 

1.408 

9.976 

68.544 

77.112 

NATIONAL  TUBE  COMPANY. 


plan  _ 
The  indicated  horse-power  of  an  engine  equals^g  QQQ  — 

aX I  n  Xp ^area  of  piston  X piston  speed     ^  in^hichp  = 

33,000  33,000 

mean  effective  pressure  in  Ibs.  per  sq.  in.;  /=  length  of 
stroke  in  f t. ;  a  —  effective  area  of  piston  in  sq.  in. ;  and 
n  —  number  of  impulse  strokes  per  minute. 

The  piston  speed  for  a  single  acting,  double  acting  or 
a  multiple  cylinder  engine  —  the  length  of  stroke  in  ft.  X 
number  of  impulse  strokes  per  minute. 


FEED-WATER  HEATERS.-(KENT). 

Percentage  of  Saving  for  Each  Degree  of  Increase  in  Tem- 
perature of  Feed-water  Heated  by  Waste  Steam. 


Initial 
Temp. 

of 
Feed. 


40 
50 
60 
70 
80 
90 
100 
110 
120 
130 
140 
150 
160 
170 
180 
190 
200 
210 


Pressure  of  Steam  in  Boiler,  Ibs.  per  sq.  in.  above 
Atmosphere. 


0       20      40      60 


.1018 


1050 

1062 


0847 
,0853 


,0867 
,0875 


.0899 
,0907 
,0915 
.0924 
,0932 
,0941 
,0950 


100     120     140     160     180 


,0844 
,0850 
,0857 
,0864 
,0872 
,0879 
.0887 


,0911 
,0920 


,0955 
,0965 
.0974 
,0984 
,0994 
,1004 
,1012 
,1024 
.1035 


,0877 
,0884 
0892 
,0900 
0908 
0917 
,0925 
,0934 
,0943 
,0952 
,0961 
,0971 
,0980 
,0990 
,1000 
,1010 
,1020 
.1031 


.0852 


.0850 


.0867  .0864 
.0874  .0872 
.08831.0879 
.0890  .0887 
.0898  .0895 
.0906  .0903 
.0914 
.0923 
.0931 
.0940 


.0912 
.0920 


0893 
0901 


.0875 


NATIONAL  TUBE  COMPANY. 


An  approximate  rule  for  the  conditions  of  ordinary 
practice  is:  A  saving  of  \%  is  made  by  each  increase  of  11° 
in  the  temperature  of  the  feed-water.  This  corresponds 
to  0.0909  per  cent,  for  each  degree. 

The  calculation  of  saving  is  made  as  follows  :  Let 
total  heat  of  1  Ib.  of  steam  at  the  boiler-pressure  =H\ 
total  heat  of  1  Ib.  of  feed-water  before  entering  the  heater 
==  Aj,  and  after  passing  through  the  heater  =  h%  ;  then 

^2—^1 
the  saving  made  by  the  heater  is  TT       /    • 

Example.  —  Given  boiler  pressure  —  100  Ibs.  gauge;  feed 
water  temperature,  original  =  60°F.  and  final  ^209°F.  ;  to 
find  the  percentage  of  saving  resulting  from  heating  the 
feed-water.  From  the  table  of  properties  of  saturated 
steam  we  find  #=1185  B.T.U.;  h±  =60—  32  =  28  B.T.U.; 
>&2=209  —  32=177  B.T.U. 

Then  the  saving  by  heater  =  ^"f1  =  ™  ~  f.  =  12.9 
rl  —  n.        HoO  —  do 


per  cent. 

To  solve  by  table  look  in  column  of  steam  pressures 
headed  "  100"  and  opposite  to  60°  in  first  column  read 
0.0864,  which  multiplied  by  (209—60  =  149)  the  increase 
of  temperature  of  feed-water,  gives  12.9  per  cent.,  as 
before. 


NATIONAL  TUBE  COMPANY.                      157 

Safe  Working  Pressures  in   Cylindrical   Shells  of    Boilers, 

Tanks,  Pipes,  etc.,  in  Pounds  per  Square  Inch. 

(KENTS  POCKET  BOOK). 

Longitudinal  seams  double-riveted. 

(Calculated  from  formula  P  =  14  000   X  thickness  -*- 

diameter.) 

$  o  .; 

DIAMETER  IN  INCHES. 

21 

30 

36 

38 

40 

42 

44 

46 

48 

50 

52 

|S| 

1 

36.5 

29.2 

24.3 

23.0 

21.9 

20.8 

19.9 

19.0 

18.2 

17.5 

16.8 

2 

72.9 

58.3 

48.6 

46.1 

43.8 

41.7 

39.8 

38.0 

36.5 

35.0 

33.7 

3 

09.4 

87.5 

72.9 

69.1 

65.6 

62.5 

59.7 

57.1 

54.7 

52.5 

50.5 

4 

45.8 

116.7 

97.2 

92.1 

87.5 

83.3 

79.5 

76.1 

72.9 

70.0 

67.3 

5 

82.3 

145.8 

121.5 

115.1 

109.4 

104.2 

99.4 

95.1 

91.1 

87.5 

84.1 

6 

7 

18.7 
255.2 

175.0 
204.1 

145.8 
170.1 

138.2 
161.2 

131.3 
153.1 

125.0 
145.9 

119.3 
139.2 

114.1 
133.2 

109.4 
127.6 

105.0 
122.5 

101.0 

117.8 

8 

291.7 

233.3 

194.4 

184.2 

175.0 

166.7 

159.1 

152.2 

145.8 

140.0 

134.6 

9 

28.1 

262.5 

218.8 

207.2 

196.9 

187.5 

179.0 

171.2 

164.1 

157.5 

151.4 

10 

364.6 

291.7 

243.1 

230.3 

218.8 

208.3 

198.9 

190.2 

182.3 

175.0 

168.3 

11 

401.0 

320.8 

267.4 

253.3 

240.6 

229.2 

218.7 

209.2 

200.5 

192.5 

185.1 

12 

437.5 

350.0 

291.7 

276.3 

262.5 

250.0 

238.6 

228.3 

218.7 

210.0 

201.9 

13 

473.9 

379.2 

316.0 

299.3 

284.4 

270.9 

258.5 

247.3 

237.0 

227.5 

218.8 

14 

410.4 

408.3 

340.3 

322.4 

306.3 

291.7 

278.4 

266.3 

255.2 

245.0 

235.6 

15 

546.9 

437.5 

364.6 

345.4 

328.1 

812.5 

298.3 

285.3 

273.4 

266.5 

252.4 

16 

583.3 

466.7 

388.9 

368.4 

350.0 

333.3 

318.2 

304.4 

291.7 

280.0269.2 

|1| 

DIAMETER  IN  INCHES. 

IS1"1  fl 

54 

60 

66 

72 

78 

84 

90 

96 

102 

108 

120 

h.2  rt 

t 

16.2 

1476 

IsTs 

1272 

1172 

Io74 

977 

Ti 

~87~6 

~87l 

7~3 

2 

32.4 

29.2 

26.5 

24.3 

22.4 

20.8 

19  '.4 

18.2 

17.2 

16.2 

14  '.6 

3 

48.6 

43.7 

39.8 

36.5 

33.7 

31.3 

29.2 

27.3 

25.7 

24.3 

21.9 

4 

64.8 

58.3 

53.0 

48.6 

44.9 

41.7 

38.9 

36.5 

34.3 

32.4 

29.2 

5 

81.0 

72.9 

66.3 

60.8 

56.1 

52.1 

48.6 

45.6 

42.9 

40.5 

36.5 

6 

97.2 

87.5 

79.5 

72.9 

67.3 

62.5 

58.3 

54.7 

51.5 

48.6 

43.8 

7 

113.4 

102.1 

92.8 

85.1 

78.5 

72.9 

68.1 

63.8 

60.0 

56.7 

51.0 

8 

129.6 

116.7 

106.1 

97.2 

89.7 

83.3 

77.8 

72.9 

68.6 

64.8 

58.3 

9 

145.8 

131.2 

119.3 

109.4 

101.0 

93.8 

87.5 

82.0 

77.2 

72.9 

65.6 

10 

162.0 

145.8 

132.6 

121.5 

112.2 

104.2 

97.2 

91.1 

85.8 

81.0 

72.9 

11 

178.2 

160.4 

145.8 

133.7 

123.4 

114.6 

106.9 

100.3 

94.4 

89.1 

80.2 

12 

194.4 

175.C 

159.1 

145.8 

134.6 

125.0 

116.7 

109.4 

102.9 

97.2 

87.6 

13 

210.7 

189.6 

172.4 

158.  C 

145.8 

135.4 

126.4 

118.  S 

llt.fi 

105.3 

94.8 

14 

226.  S 

204.  S 

185.6 

170.1 

157.1 

145.8 

136.1 

127.6 

120.1 

113.4 

102.1 

15 

243.1 

218.  r 

198.  J 

182.1 

168.2 

156.  S 

145.8 

136.7 

128.7 

121.  C 

109.4 

16 

259.2 

233.  1 

212.1 

194.4 

179.  J 

166.7 

155.6 

145.8 

137.2 

129.6 

116.7 

,. 

NATIONAL  TUBE  COMPANY. 


The  preceding  table  has  been  computed  for  externally- 
fired  boilers,  with  longitudinal  seams  double-riveted  and 
having  an  efficiency  of  0.7.  A  factor  of  safety  of  5.5  has 
been  assumed  for  steel  of  55,000  Ibs.  tensile  strength. 


SIZES  OF  CHIMNEYS  FOR  STEAM  BOILERS. 

BY  WILLIAM  KENT,  M.  E. 

The  accompanying  tabe  of  sizes  of  chimneys  for  various 
horse  powers  of  boilers  is  based  on  the  following  data: 
.    1.  The  draught  power  of  the  chimney  varies  as  the 
square  root  of  the  height* 

2.  The  retarding  of  the  ascending  gases  by  friction 
may  be  considered  as  equivalent  to  a  diminution  of  the 
area  of  the  chimney,  or  to  a  lining  of  the  chimney  by  a 
layer  of  gas  which  has  no  velocity.    The  thickness  of 
this  lining  is  assumed  to  be  two  inches  for  all  chimneys, 
or  the  diminution  of  area  equal  to  the  perimeter  X  two 
inches  (neglecting  the  overlapping  of  the  corners  of  the 
lining).     Expressed  algebraically,  let  D  —  diameter,  A  — 
area,  E=  effective  area. 

For  square  chimneys,   E  =  D9—  3%  =  ^  ~      .  ^  • 

For  round  chimneys,  E=  n( D*— ^  \=  ^4— 0.592  |/^ 

For  simplifying  calculations,  the  coefficient  of  |/  A 
may  be  taken  as  0.6  for  both  square  and  round  chimneys, 
and  the  formula  becomes 

E  =  A  —  0.6  V~A- 

3.  The  power  varies  directly  as  this  effective  area  E. 

4.  A  chimney  80  feet  high,  42  inches  diameter,  has 
been  found  to  be  sufficient  to  cause  a  rate  of  combustion 


NATIONAL  TUBE  COMPANY. 


of  120  pounds  of  coal  per  hour  per  square  foot  of  area  of 
chimney,  or  if  the  grate  area  is  to  the  chimney  area  as  8 
to  1,  a  combustion  of  15  pounds  of  coal  per  square  foot 
of  grate  per  hour.  This  is  fair  practice  for  a  boiler  of 
modern  type,  in  which  flues,  or  tubes  are  of  moderate 
diameter,  gas  passages  circuitous,  and  heating  surface 
extensive  in  proportion  to  rate  of  combustion,  so  as  to 
cool  the  chimney  gases  to  400°  or  500°  Fahr.  and  produce 
high  economy. 

5.  A  chimney  should  be  proportioned  so  as  to  be  capa- 
ble of  giving  sufficient  draught  to  cause  the  boiler  to  de- 
velop much  more  than'  its  rated  power,  in  case  of  emerg- 
encies, or  to  cause  the  combustion  of  5  pounds  of  fuel 
per  rated  horse-power  of  boiler  per  hour. 

Conditions  4  and  5  being  assumed,  the  80  feet  X  42  in- 
ches chimney,  9.62  square  feet  area,  will  cause  the  com- 
bustion of  9.62  X  120  =  1154.4  pounds  of  coal  per  hour,  or 
at  5  pounds  of  coal  per  horse-power  per  hour,  is  rightly 
proportioned  for  231  horse-power  of  boilers. 

The  power  of  the  chimney  varying  directly  as  the  ef- 
fective area,  JS,  and  as  the  square  root  of  the  height,  h, 
the  formula  for  horse-power  of  boiler  for  a  given  size  of 
chimney  will  take  the  form,  — 

HP.  =  CE  \/  h,  in  which  C  is  a  constant. 
For  the  80'  X  42"  chimney  ,**&& 

t  \/  A  =7.76  square  feet. 


V~h=  8.944  feet. 

Substituting  these  values  in  the  formula  it  becomes  — 
231  =  Cx  7.76  X  8.944, 
whence  C-  3.33, 


NATIONAL  TUBE  COMPANY. 


and  the  formula  for  horse-power  is 
HP.  =  3.33  E  \/~7T,  or,  HP.  =  3.33  (,4—0.6 

If  the  horse-power  of  boiler  is  given,  to  find  the  size  of 
chimney,  the  height  being  assumed, 

0.3  HP. 


For  round  chimneys,  diameter  of  chimney  =  Diam. 
of  ^  +  4". 

For  square  chimneys,  side  of  chimney  —  |/  E  -f-  4". 

In  the  formulae  and  table  no  account  has  been  taken  of 
the  difference  which  is  believed  by  some  authorities  to 
exist  in  the  efficiencies  of  round  and  square  chimneys  of 
equal  area,  nor  of  the  differences  of  friction  and  of  rate 
of  cooling  of  the  gases  in  -iron  and  in  brick  chimneys. 
Should  experimental  data  of  these  differences,  or  of  the 
effect  of  infiltration  of  air  into  brick  chimneys,  be  ob- 
tained in  future,  the  formulae  and  table  may  be  corrected 
accordingly. 


NATIONAL  TUBE  COMPANY. 


ivalent 
quare 
imney. 
ofSquare 
inches 


S  FOR  ST 

(KENT.) 

(Assuming  1  H 


SIZE  OF 


Equ 
S 
Chi 
ide 


J  II  p5 
I**)  >« 


w<. 


SJSSSS 


•y  -bs 
• 


AIR. 


NATIONAL  TUBE  COMPANY. 


AIR. 

Air  consists  of  a  mechanical  mixture  of  the  two  gases 
oxygen  and  nitrogen  in  the  ratio  of  20.7  parts  of  the 
former  to  79.3  of  the  latter  by  volume,  and  23  of  the  for- 
mer to  77  of  the  latter  by  weight.  In  its  natural  state  it 
contains  small  quantities  of  various  substances,  such  as 
moisture,  carbon  dioxide,  CO2,  the  lately  discovered  ele- 
ment argon,  etc. 

The  weight  of  dry  air  at  32° F.  and  atmospheric  pressure 
(14.7  Ibs.  per  sq.  in.)  is  0.0807  Ibs.  per  cu.  ft.;  from  which 
the  volume  of  one  pound=12.4  cu.  ft.  At  other  tem- 
peratures and  pressures  its  weight  in  Ibs.  per  cu.  ft.  is 
^~459^+t'  *n  wl"ck  ^—reading  of  barometer  in  inches 
and  ^temperature  F. 

The  absolute  zero  of  temperature,  on  the  Fahr.  scale  is 
492°  below  32°,  or— 460°F. 

The  absolute  temperature  then  is  obtained  by  adding 
460°  to  the  temperature  as  read  from  the  Fahr.  scale. 
Thus  60°F.  =  60° +  460°  =520°  absolute;  and— 20°F.= 
— 20°-f460°=440°  absolute. 

Mechanical  equivalent  of  heat.— Heat  energy  and  me- 
chanical energy  are  mutually  convertible,  that  is,  a  unit 
of  heat  requires  for  its  production,  and  produces  by  its 
disappearance,  a  definite  amount  of  mechanical  energy, 
namely,  778  foot-pounds  of  work  for  each  British  ther- 
mal unit. 

Boyle's  law  states  that  the  product  of  the  pressure  and 
volume  of  a  portion  of  gas  is  constant  so  long  as  the 
temperature  is  constant,  that  \s,pv=.c,  in  which  p= pres- 
sure in  Ibs.  per  sq.  ft.  and  z/=:volume  in  cu.  ft.  For  air 
at  32°F,,  this  constant  quantity  is  26,200  foot-pounds,  or 
pv=2Q,2QQ  ft.  Ibs. 

Charles'  and  Gay  Lussac's  law  states  that  when  the  pres- 
sure is  constant  all  gases  expand  alike  for  the  same  in- 
crease of  temperature.  The  amount  of  this  expansion 


NATIONAL  TUBE  COMPANY. 


between  32°  and  212°F,  is  0.365  of  the  original  volume: 
and  for  each  degree  it  equals  0.365-^180=0.00203.  Simi- 
liarly,  when  the  volume  remains  constant  the  pressure 
varies  in  the  above  ratio. 

Combining  Boyle's  and  diaries'  laws  we  see  that  the  pro- 
duct of  the  pressure  and  volume  of  a  portion  of  gas  is 
proportional  to  the  absolute  temperature.  Thus,  -j~  — 
£,  in  which  p  and  ^^absolute  pressures  (that  is  pres- 
sures above  a  vacuum)  in  Ibs.  per  sq.  ft.;  v  and  v^—  vol- 
umes in  cu.  ft.;  T  and  7\=absolute  temperatures. 

Transforming  the  above  equation  and  substituting  32 
for  7\  and  26,200  for  p^,  we  get 


=53.2  T. 


The  specific  heat  of  a  gas  is  the  quantity  of  heat,  in  heat 
units,  necessary  to  raise  the  temperature  of  one  pound  of 
the  gas  through  one  degree  of  temperature. 

The  specific  heat  of  air  at  constant  pressure  is  cp=0.238 
and  at  constant  volume  is  cv  =0.169  British  thermal  unit. 

Adiabatic  expansion  or  compression  of  a  gas  means  that 
the  gas  is  expanded  or  compressed  without  transmission 
of  heat  to  or  from  the  gas.  This  would  be  the  case  were 
the  expansion  or  compression  to  take  place  in  an  abso- 
lutely non-conducting  cylinder,  in  which  case  the  tem- 
perature, pressure  and  volume  would  vary  as  indicated 
by  the  following  formulae. 

v2      /PA0.71.  p.      /vAl.41.  T_,_/vA0.41. 

vI=VpV  Pi-^v,'  Ti-Vv./ 

v2_/TA2.46.  p,_/T,\3.46.  T^/pAO.Sg. 

v1      \T,/  Pi7^T1/  Tx      Vpiy 

in  which  plf  Vj  and  Tx=initial  absolute  pressure,  vol- 
ume and  absolute  temperature  and  p2,  v2  and  T2=final 
absolute  pressure,  volume  and  absolute  temperature  of 
the  gas. 


D 

166                      NATIONAL  TUBE  COMPANY. 

Table  for  Adiabitic  Compression  or  Expansion  of  Air. 

(PROC.,  INST.  M.  E.,  Jan.  1881,  p.  123.) 

Absolute  Pressure. 

Absolute 
Temperature. 

Volume. 

pa 

P1 

T2 

Ti 

V, 

V2 

?" 

P2 

T, 

T7 

"v; 

"vT 

1.2 

8.33 

1.054 

.948 

1.138 

8.79 

1.4 

7.14 

1.102 

.907 

1.270 

.788 

1.6 

.625 

1.146 

.873 

1.396 

.716 

1.8 

.556 

1.186 

.843 

1.518 

.659 

2.0 

.500 

1.222 

.818 

1.636 

.611 

2.2 

.454 

1.257 

.796 

1.750 

.571 

2.4 

.417 

1.289 

.776 

1.862 

.537 

2.6 

.385 

1.319 

.758 

1.971 

.507 

2.8 

.357 

1.348 

.742 

2.077 

.481 

3.0 

.333 

1.375 

.727    . 

2.182 

.458 

3.2 

.312 

1.401 

.714 

2.284 

.438 

3.4 

.294 

1.426 

.701 

2.384 

.419 

3.6 

.278 

1.450 

.690 

2.483 

.403 

3.8 

.263 

1.473 

.679 

2.580 

.388 

4.0 

.250 

1.495 

.669 

2.676 

.374 

4.2 

.238 

1.516 

.660 

2.770 

.361 

4.4 

.227 

1.537 

.651 

2.863 

.349 

4.6 

.217 

1.557 

.642 

2.955 

.338 

4.8 

.208 

1.576 

.635 

3.046 

.328 

5.0 

.200 

1.595 

.627 

3.135 

.319 

6.0 

.167 

1.681 

.595 

3.569 

.280 

7.0 

.143 

1.758 

.569 

3.981 

.251 

8.0 

.125 

1.828 

.547 

4.377 

.228 

9.0 

.111 

1.891 

.529 

4.759 

.210 

10.0 

.100 

1.950 

.513 

5.129 

.195 

"Work  of  adiabatic  compression  of  air.—  If  air  is  compressed 

from  a  volume  vt  and  pressure  pl  to  a  volume  v2  and 

pressure  pa,  in  a  non-conducting  cylinder  without  clear- 

ance, the  work  involved  in  delivering  one  pound  is  as 

follows: 

Work  of  compression    =   2.46  pt  Vj  [(v^)0'41"1]    = 

NATIONAL  TUBE  COMPANY.  167 

Work  of  expulsion     =     pav3     =     p^  (£?)  °-29    . 

Total  work  is  the  sum  of  the  work  of  compression  and 
expulsion  less  the  work,  p^,  of  the  atmosphere  done  on 
the  piston  during  admission,  or 

Total  work    =    3.46  plVl  [(P?)0'29-!]. 

The  mean  effective  pressure  equals  the  total  work  -f-  the 
initial  volume,  vx,  or 


Isothermal  expansion  or  compression  of  a  gas  means  that 
the  gas  is  expanded  or  compressed  with  the  addition  or 
rejection  of  sufficient  heat  to  maintain  the  temperature 
constant.  In  this  case,  the  temperature  being  constant, 
the  pressure  and  volume  will  vary  according  to  Boyle's 
law,  namely 

pv=C, 

in  which  /^absolute  pressure  in  Ibs.  per  sq.  ft.,  v=.  vol- 
ume in  cu.  ft.,  and  C=a  constant  depending  upon  the 
temperature.  For  a  temperature  of  32  °F.  this  constant 
is  26,200  ft.  Ibs.,  and  for  isothermals  corresponding  to 
other  temperatures  it  may  be  found  from  the  formula 
0=53.2  7",  in  which  Z=the  absolute  temperature  of  the 
isothermal. 

Work  of  isothermal  compression  of  air.  —  If  air  is  com- 
pressed from  a  volume  Vj  and  pressure  pj  to  a  volume  va 
and  pressure  p3,  in  a  cylinder  without  clearance,  in  such 
manner  as  to  keep  the  temperature  constant,  the  work 
involved  in  delivering  one  pound  is  as  follows: 

Work  of  compression     =    PiVt  log     Xi. 
Work  of  expulsion         =    pava  =   pjV^ 
The  total  work  then  is  the  sum  of  the  work  of  com- 
pression and  expulsion  less  the  work,  p^,  of  the  atmos- 
phere done  on  the  piston  during  admission,  or 

Total  work  =  px  vx  log  e  Xi  +  p^  —  p^  =  p^ 


^r* 


168                       NATIONAL  TUBE  COMPANY. 

In  this  formula  Naperian,  or  hyperbolic,  logarithms 

must  be  used.     These  may  be  obtained  from  the  common 

logarithms  by  multiplying  by  the  constant  2.303. 

The  mean  effective  pressure  equals  the  total  work  -f- 

the  initial  volume,  v1?  or  px  log    ^i. 

Volumes  Mean  Pressures  per  Stroke,  Temperatures,  etc., 

in  the  Operation  of  Air-compression  from  from  J  Atmosphere 

and  60°  Fahr.     (F.  RICHARDS,  Am.  Mach.,  March  30,  1893.) 

i 

•z  ,   • 

A 

S.^aj 

£_T3 

V 

5!  ^-^ 

<u 

$**  ° 

£03 

a;U  ° 

<u  u.'o 

£!  8  a  2 

goo 

S-is'o 

rt  w 

1 

s*+! 

a<8 

^C/DQ^ 

^wo 

0/^8 

cx 

a 

•!•«§ 

"o     g 

S  s.^a 

jjjkS 

S'OQ 

< 

><•£ 

^ 

ga^h 

sa< 

h     G 

1 

2 

3 

4 

5 

6 

7 

0 

1 

1 

1 

0 

0 

60° 

1 

1.068 

.9363 

.950 

.96 

.97 

71 

2 

1.136 

.8803 

.910 

1.87 

1.91 

80 

3 

1.204 

.8305 

.876 

2.72 

2.80 

89 

4 

1.272 

.7861 

.840 

3.53 

3.67 

98 

5 

1.340 

.7462 

.810 

4.30 

4.50 

106 

10 

1.680 

.5952 

.690 

7.62 

8.27 

145 

15 

2.020 

.4950 

.606 

10.33 

11.51 

178 

20 

2.360 

.4237 

.543 

12.62 

14.40 

207 

25 

2.700 

.3703 

.494 

14.59 

17.01 

234 

30 

3.040 

.3289 

.453 

16.34 

19.40 

252 

35 

3.381 

.2957 

.420 

17.92 

21.60 

281 

40 

3.721 

.2687 

.393 

19.32 

23.66 

302 

45 

4.061 

.2462 

.370 

20.57 

25.59 

321 

50 

4.401 

.2272 

.350 

21.69 

27.39 

339 

55 

4.741 

.2109 

.331 

22.76 

29.11 

357 

60 

5.081 

.1968 

.314 

23.78 

30.75 

375 

65 

5.423 

.1844 

.301 

24.75 

32.32 

389 

70 

5.762 

.1735 

.288 

25.67 

33.83 

405 

75 

6.102 

.1639 

.276 

26.55 

35.27 

420 

!<n  <  n 

NATIONAL  TUBE  COMPANY. 


Volumes,  Mean  Pressures  per  Stroke,  Temperatures,  etc. 

(CONTINUED.) 


OJ 

B 

5  i  ^ 

5    -a 

§  -a  £ 

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a_3 

h     § 

1 

2 

3 

4 

5 

6 

7 

80 

6.412 

.1552 

.2670 

27.38 

36.64 

432° 

85 

6.782 

.1474 

.2566 

28.16 

37.94 

447 

90 

7.122 

.1404 

.2480 

28.89 

39.18 

459 

95 

7.462 

.1340 

.2400 

29.57 

40.40 

472 

100 

7.802 

.1281 

.2324 

30.21 

41.60 

485 

105 

8.142 

.1228 

.2254 

30.81 

42.78 

496 

110 

8.483 

.1178 

.2189 

31.39 

43.91 

507 

115 

8.823 

.1133 

.2129 

31.98 

44.98 

518 

120 

9.163 

.1091 

.2073 

32.54 

46.04 

529 

125 

9.503 

.1052 

.2020 

33.07 

47.06 

540 

130 

9.843 

.1015 

.1969 

33.57 

48.10 

550 

135 

10.183 

.0981 

.1922 

34.05 

49.10 

560 

140 

10.523 

.0950 

.1878 

34.57 

50.02 

570 

145 

10.864 

.0921 

.1837 

35.09 

51  .00 

580 

150 

11.204 

.0892 

.1796 

35.48 

51.89 

589 

160 

11.880 

.0841 

.1722 

36.29 

53.65 

607 

170 

12.560 

.0796 

.1657 

37.20 

55.39 

624 

180 

13.240 

.0755 

.1595 

37.96 

57.01 

640 

190 

13.920 

.0718 

.1540 

38.68 

58.57 

657 

200 

14.600 

.0685 

.1490 

39.42 

60.14 

672 

Combined  compression  of  air,  is  compression  under  con- 
ditions that  permit  of  some  withdrawal  of  heat  during 
compression,  but  not  sufficient  to  keep  the  temperature 
of  the  air  constant.  In  this  case  the  compression  curve 
lies  between  the  isothermal  and  adiabatic  curves,  and  the 
relation  of  pressure  to  volume  may  be  expressed  by  the 
formula 


P 


=  C, 


in  which  p  =  absolute  pressure  in  Ibs,  per  sq.  ft.;  v  = 
volume  in  cu.  ft.;  C  =  a  constant;  and  n  =  an  exponent 
whose  value  may  vary  from  1,  that  for  isothermal,  to 
1.41,  that  for  adiabatic  compression  or  expansion, 


NATIONAL  TUBE  COMPANY. 


"Work  of  combined  compression. — If  air  is  compressed 
from  a  volume  vx  and  pressure  pl  to  a  volume  v2  and 
pressure  p2,  in  a  cylinder  without  clearance,  the  work 
involved  in  delivering  one  pound  is  as  follows: 


Work  of  compression    =    (p2v2  —  PiVj) = 

v3  Vl  —  va 

53.2  (T3  —  TA) . 

Vi— va 

Work  of  expulsion  =  Psv2- 

The  total  work  is  the  sum  of  the  work  of  compression 
and  expulsion  less  the  work,  p^,  done  by  the  atmos- 
phere on  the  piston  during  admission,  or 

Total  work  =  (p3v3  —  PiVx) \-  psv2  —  p^ 


=  (Psv2  —  pjVi) . 

Vi— v3 


NATIONAL  TUBE  COMPANY. 


Temperature  Fahrenheit 

The  results   of  air  compression  and   expansion    are 
shown  by  the  above  diagram. 


NATIONAL  TUBE  COMPANY. 


Useful  information  on  Volume  and  Pressure  Curves  of  Air. 
(FROM  COMPRESSED  AIR  MAGAZINE.) 

In  the  diagram  on  the  preceding  page,  the  figures  at 
the  left  indicate  pressures  in  atmospheres  above  a 
vacuum  ;  the  corresponding  figures  at  the  right  denote 
pressures  in  pounds  per  square  inch,  by  the  gauge.  At 
the  top  are  volumes  from  one-tenth  to  one.  At  the 
bottom,  degrees  of  temperatures  from  zero  to  1,000 
degrees  Fahrenheit.  The  two  curves  which  begin  at  the 
lower  left  hand  corner  and  extend  to  the  upper  right  are 
the  lines  of  compression,  or  expansion.  The  upper  one 
being  the  "Adiabatic"  curve,  or  that  which  represents 
the  pressure  at  any  point  on  the  stroke,  with  the  heat 
developed  by  compression  remaining  in  the  air ;  the 
lower  is  the  "Isothermal,"  or  the  pressure  curve,  when 
the  heat  of  compression  is  withdrawn  so  as  to  keep 
the  temperature  constant.  The  three  curves  which  begin 
at  the  lower  right  hand  corner  and  rise  to  the  left  are 
heat  curves,  and  represent  the  increase  of  temperature 
corresponding  to  different  pressures  and  volumes,  as- 
suming in  one  case  that  the  temperature  of  the  air  before 
admission  to  the  compressor  is  zero,  in  another  sixty  de- 
grees, and  in  another  one  hundred  degrees. 

Beginning  with  the  adiabatic  curve,  we  find  that  for 
one  volume  of  air,  when  compressed  without  cooling,  the 
curve  intersects  the  first  horizontal  line  at  a  point  be- 
tween 0.6  and  0.7  volume,  the  gauge  pressure  being  14.7 
pounds.  If  we  assume  that  this  air  was  admitted  to  the 
compressor  at  a  temperature  of  zero,  it  will  reach  about 
100°  when  the  gauge  pressure  is  14.7  pounds.  If  the  air 
had  been  admitted  to  the  compressor  at  60°,  it  would 
register  about  176°  at  14.7  pounds  gauge  pressure.  If 
the  air  were  100°  before  compression,  it  would  go  up  to 
about  230°  at  this  pressure.  Following  this  adiabatic 
curve  until  it  intersects  line  No.  5,  representing  a  pres- 
sure of  five  atmospheres  above  a  vacuum  (58.8  pounds 


NATIONAL  TUBE  COMPANY.  173 

gauge  pressure),  we  see  that  the  total  increase  of  tem- 
perature on  the  zero  heat  curve  is  about  270°;  for  the 
60°  curve  it  is  about  370°,  and  for  the  100°  curve  it  is 
435°.  The  diagram  shows  that  when  a  volume  of  air  is 
compressed  adiabatically  to  21  atmospheres  (294  pounds 
gauge  pressure),  it  will  occupy  a  volume  a  little  more 
than  one-tenth;  the  total  increase  of  temperature  with 
an  initial  temperature  of  zero,  is  about  650°;  with  60° 
initial  temperature  it  is  800°  and  with  100°  initial  it  is 
900°.  It  will  be  observed  that  the  zero  heat  curve  is 
flatter  than  the  others,  indicating  that  when  free  air  is 
admitted  to  a  compressor  cold,  the  relative  increase  of 
temperature  is  less  than  when  the  air  is  hot.  This  points 
to  the  importance  of  low  initial  temperature.  It  is  plain 
that  a  high  initial  temperature  means  a  higher  tempera- 
ture throughout  the  stroke  of  a  compressor.  The  dia- 
gram gives  the  loss  of  temperature  during  compression 
from  initial  temperatures  of  0°,  60°,  100°.  If  we  compare 
the  compression  line  from  zero  with  the  compression 
line  from  100°,  we  observe  that  in  compressing  the  air 
from,  say  1  atmosphere  to  10  atmospheres,  the  original 
difference,  which  .at  the  start  was  only  100°,  has  now 
been  about  doubled;  that  is,  it  has  reached  200°,  and  in 
carrying  the  compression  to  20  atmospheres,  the  differ- 
ence now  becomes  about  250°.  Each  horizontal  division 
represented  by  the  figures  at  the  bottom  is  equal  to  100°, 
and  the  space  between  any  two  adjacent  horizontal  lines 
may  be  sub-divided  into  100  equal  parts  representing  1° 
each. 

Where  there  is  a  system  of  cooling  the  air  during 
compression,  the  lines  on  the  indicator  cards  can  be 
traced  between  the  adiabatic  and  isothermal  curves  on 
the  diagram. 

For  all  practical  purposes  in  using  this  diagram,  it  is 
best  to  follow  the  adiabatic  curve  in  all  determinations, 
except  where  the  exact  pressure  line  is  known.  This 
diagram  will  be  found  convenient  to  those  who  are  called 
upon  to  figure  the  pressure  at  different  points  in  the 


NATIONAL  TUBE  COMPANY. 


stroke  of  an  air  compressor,  and  it  points  out  the  com- 
mon error  of  neglecting  to  take  into  consideration  in  one's 
figures  the  fact  that,  at  the  beginning  of  the  stroke,  one 
atmosphere  in  volume  already  exists.  Beginning  at  the 
lower  left  hand  corner,  the  adiabatic  pressure  curve 
intersects  the  first  horizontal  line  at  that  point  in  the 
stroke  when  the  pressure  on  the  gauge  will  register  14.7 
pounds. 

The  next  horizontal  line  shows  where  the  gauge  reaches 
29.4  pounds,  and  it  is  evident  here  that  the  piston  of  an 
air  compressor  travels  much  farther  in  reaching  14.7 
pounds  than  in  doubling  that  pressure  or  in  reaching 
29.4  pounds;  thus  an  air  compressor  is  an  engine  of  un- 
evenly distributed  resistance.  During  the  early  stages 
of  the  stroke  it  has  a  slowly  accumulating  load  to  carry, 
while  later  on  this  load  is  multiplied  very  rapidly.  This 
is  one  of  the  reasons  for  heavy  flywheels  in  air  com- 
pressors. 


NATIONAL  TUBE  COMPANY  175 


Compressed  Air* 


EFFECT    OF     COMPOUNDING,    COOUNG,    INTER-COOKING, 
AFTER-COOKING  AND  REHEATING. 

(From  Compressed  Air  Magazine.) 

Builders  of  air  compressors  and  those  who  use  com- 
pressed air  will  agree  that  the  problem  of  heating  or 
cooling  air  is  a  difficult  one.  Hot  air  in  the  cylinder  of 
an  air  compressor  means  a  reduction  in  the  efficiency  of 
the  machine.  The  trouble  is,  that  there  is  not  sufficient 
time  during  the  stroke  to  cool  thoroughly  by  any  avail- 
able means.  Water-jacketing  is  the  generally  accepted 
practice,  but  it  does  not  by  any  means  effect  through 
cooling.  The  air  in  the  cylinder  is  so  large  in  volume 
that  but  a  fraction  of  its  surface  is  brought  in  contact 
with  the  jacketed  parts.  Air  is  a  bad  conductor  of  heat 
and  takes  time  to  change  its  temperature.  The  piston 
while  pushing  the  air  towards  the  head  rapidly  drives  it 
away  from  the  jacketed  surfaces;  so  that  little  or  no 
cooling  takes  place.  This  is  especially  true  of  large 
cylinders  where  the  economy  effected  by  water-jackets 
is  considerably  less  than  in  small  cylinders.  Engineers 
who  are  shown  indicator  cards  from  large  air  compres- 
sors with  pressure  lines  running  away  from  the  adiabatic, 
naturally  regard  them  with  suspicion  and  look  for  leaks 
past  the  piston  or  through  the  valves.  Such  leaks  will 
explain  many  isothermal  cards,  and  until  something 
better  than  a  water-jacket  is  devised,  it  is  well  to  seek 
economy  in  air  compression  through  compounding. 

The  great  advantage  of  compounding  is  in  the  fact 
that  the  inter-cooler,  which  should  always  be  used  with 
compound  machines,  effects  a  larger  saving  by  cooling 
and  thereby  causing  the  air  to  shrink  in  volume  between 
the  stages.  A  properly  designed  inter-cooler  should 
reduce  the  temperature  of  the  air  back  to  the  orginal 


NATIONAL  TUBE  COMPANY. 


point,  that  is,  to  the  temperature  of  the  intake  air.  It 
can  even  do  more  than  this,  especially  in  winter,  when 
the  water  used  in  the  inter-color  is  of  low  temperature. 
A  simple  coil  of  pipe  submerged  in  water  is  not  an 
effective  inter-cooler,  because  the  air  passes  through  tbe 
coil  too  rapidly  to  be  cooled  to  the  core,  and  such  inter- 
coolers  do  not  sufficiently  split  up  the  air  to  enable  it  to 
be  cooled  rapidly.  This  splitting  up  of  air  is  an  import- 
ant point.  A  nest  of  tubes  carrying  water  and  arranged 
so  that  the  air  is  forced  between  and  around  the  tubes  is 
an  efficient  form  of  inter-cooler. 

Receiver  inter-coolers  are  more  efficient  than  those  of 
the  common  type  because  the  air  is  given  more  time  to 
pass  through  the  cooling  stages  and  because  of  the  free- 
dom from  wire  drawing  which  may  take  place  in  inter- 
coolers  of  small  volumetric  capacity. 

After-coolers  are  in  some  installations  as  important  as 
inter-coolers.  An  after-cooler  serves  to  reduce  the  tem- 
perature of  the  air  after  the  final  compression.  In  doing 
this  it  serves  as  a  drier,  reducing  the  temperature  of  air 
to  the  dew  point,  thus  abstracting  moisture  before  the  air 
is  started  on  its  journey.  In  cold  weather  with  air  pipes 
laid  over  the  ground  an  after-cooler  may  prevent  accu- 
mulation of  frost  in  the  interior  walls  of  the  pipes,  for 
where  the  hot  compressed  air  is  allowed  to  cool  gradually 
the  walls  of  the  pipe  in  cold  weather  act  like  a  surface 
condenser  and  moisture  may  be  deposited  on  the  inside, 
for  the  same  reason  that  we  have  frost  on  the  inner  side 
of  a  window  pane.  Another  advantage  of  the  after- 
cooler  is  that  it  keeps  the  temperature  of  the  line  pipe 
uniform,  otherwise  this  pipe  will  be  hottest  near  the  com- 
pressor, gradually  cooling  down  and  being  thus  subject 
to  irregularities  of  expansion  and  contraction. 

The  following  table  will  serve  to  illustrate  the  large 
saving  that  it  is  possible  to  effect  by  compounding. 
This  table  gives  the  percentage  of  work  lost  by  the  heat 
of  compression,  taking  isothermal  compression,  or  com- 
pression without  heat,  as  a  base. 


NATIONAL  TUBE  COMPANY. 


One  Stage. 

Two  Stage. 

Four  Stage. 

3 

a  g 

a  3 

.si. 

(3*3 

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ft'S 

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13.12 

5.04 

4.80 

100 

38. 

27.58 

17.10 

14.62 

8.00 

7.41 

200 

52.35 

34.40 

23.20 

18.88 

9.01 

8.27 

400 

68.60 

40.75 

29.70 

22.90 

12.40 

11.04 

600 

83.75 

44.60 

32.65 

24.60 

15.06 

13.10 

800 

90. 

47.40 

35.80 

26.33 

16.74 

14.32 

1000 

96.80 

49.20 

39.00 

28.10 

16.90 

14.45 

1200 

106.15 

51.60 

40.00 

28.60 

17.45 

14.85 

1400 

108. 

52. 

41.60 

29.4 

17.70 

15.00 

1600 

110. 

53.3 

42.90 

30.0 

18.40 

15.54 

1800 

116.80 

54. 

44.40 

30.6 

19.12 

16.05 

2000 

121.70 

54.8 

44.60 

30.8 

20.00 

16.65 

In  the  above  table  no  account  is  taken  of  jacket 
cooling,  it  being  a  well  known  fact  among  pneumatic 
engineers  that  water  jackets,  especially  cylinder  jackets, 
though  useful  and  perhaps  indispensable,  are  not  efficient 
in  cooling,  especially  so  in  large  compressors.  The 
volume  of  air  is  so  great  in  proportion  to  the  surface  ex- 
posed and  at  the  time  of  compression  so  short,  that  little 
or  no  cooling  takes  place.  Jacketed  heads  are  useful 
auxiliaries  in  cooling,  but  it  has  become  an  accepted 
theory  among  engineers  that  compounding  or  stage  com- 
pression is  more  fertile  as  a  means  of  economy  than  any 
other  system  that  has  yet  been  devised.  The  two  and 
four  stage  figures  in  this  table  (columns  3  and  4),  are 
based  on  reduction  to  atmospheric  temperature,  or  60° 
Fahrenheit,  between  stages.  A  rule  which  might  be 


NATIONAL  TUBE  COMPANY. 


observed  to  advantage  among  engineers  is  to  specify  that 
the  manufacturers  should  supply  a  compressor  with 
coolers  provided  with  one  square  foot  of  tube  cooling 
surface  for  every  ten  cubic  feet  of  free  air  furnished  by 
the  compressor  when  running  at  its  normal  speed. 

Referring  again  to  the  table,  we  learn  that  when  air  is 
compressed  to  100  pounds  pressure  per  square  inch  in  a 
single  stage  compressor  without  cooling,  the  heat  loss 
may  be  thirty-eight  (38)  per  cent.  This  condition,  of 
course,  does  not  exist  in  practice,  except  perhaps,  at 
exceedingly  high  speeds,  as  there  will  be  some  absorp- 
tion of  heat  by  the  exposed  parts  of  the  machine.  It  is 
safe,  however,  to  say  that  in  large  air  compressors  that 
compress  in  a  single  stage  up  to  100  pounds  gauge 
pressure,  the  heat  loss  reaches  thirty  (30)  per  cent.  This, 
as  shown  by  the  table,  may  be  cut  down  more  than  one- 
half  by  compressing  in  two-stages,  and  with  three-stages 
this  loss  is  brought  down  to  eight  (8)  per  cent,  theo- 
retically, and  perhaps  to  three  or  five  (3  or  5)  per  cent, 
in  practice.  As  higher  pressures  are  used,  the  gain  by 
compounding  is  greater. 


Efficiency  of  Air  Compressors  at 
Different  Altitudes* 

The  altitude,  where  the  compressor  is  to  operate,  is  an 
important  factor  because  it  affects  its  capacity  to  a 
greater  or  lesser  extent,  according  to  the  elevation.  As 
the  density  of  the  atmosphere  decreases  with  the  altitude, 
a  compressor  located  at  a  high  altitude  takes  in  less 
weight  of  air  at  each  revolution,  that  is  to  say,  the  air 
being  taken  in  at  a  lower  pressure,  the  early  part  of  each 
stroke  is  occupied  in  compressing  the  air  up  to  the 
normal  pressure  of  14.7  pounds,  and  the  capacity  of  the 
air  cylinder  is  correspondingly  diminished.  The  power 


NATIONAL  TUBE  COMPANY. 


required  to  drive  the  same  compressor  is  also  less  than 
at  sea  level,  but  the  decrease  in  power  required  is  not  in 
as  great  a  ratio  as  the  reduction  in  capacity.  Therefore, 
compressors  to  be  used  at  high  altitudes  should  have  the 
steam  and  air  cylinders  properly  proportioned  to  meet 
the  varying  conditions  at  different  places. 

The  following  table  shows  the  efficiency  and  loss  in 
capacity  of  compressors  working  at  different  altitudes, 
also  the  approximate  decrease  in  power  required  as  com- 
pared with  the  same  compressor  working  at  sea  level, 
and  delivering  air  at  70  pounds  pressure  per  square  inch. 


TABLE  OF  EFFICIENCIES  AT  DIFFERENT 
ALTITUDES. 

THE  EFFICIENCY  AT  SEA  LEVEL  BEING  100  PER  CENT. 


OJ 

Barometric  Pressure. 

•c°  S~ 

g 

rt+J 

E 

O-o  .J 

1 

Inches, 

Pounds  per 

111? 

ftfl 
rt  <u 

uu 

O-i  <u  a 

•g'So 
rt£*- 

< 

Mercury. 

Square 
Inch. 

m* 

*o  <D 

c/>P-i 

$&& 

J 

Q 

1000 

28.88 

14.20 

97. 

3. 

1.8 

2000 

27.80 

13.67 

93. 

7. 

3.5 

3000 

26.76 

13.16 

90. 

10. 

5.2 

4000 

25.76 

12.67 

87. 

13. 

6.9 

5000 

24.79 

12.20 

84. 

16. 

8.5 

6000 

23.86 

11.73 

81. 

19. 

10.1 

7000 

22.97 

11.30 

78. 

22. 

11.6 

8000 

22  11 

10.87 

76. 

24. 

13.1 

9000 

21.29 

10.46 

73. 

27! 

14.6 

10000 

20.49 

10.07 

70. 

30. 

16.1 

11000 

19.72 

9.70 

68. 

32. 

17.6 

12000 

18.98 

9.34 

65. 

35. 

19.1 

13000 

18.27 

8.98 

63. 

37. 

20.6 

14000 

17.59 

8.65 

60. 

40. 

22.1 

15000 

16.93 

8.32 

58. 

42. 

23.5 

180 


NATIONAL  TUBE  COMPANY. 


Horse-power  Required  to  Compress  JOO  Cubic  Feet  Free  Air, 
from  Atmospheric  to  Various  Pressures. 


Gauge 
Pressure, 
Pounds. 

One-Stage 
jCompression, 
D.  H.  P. 

Gauge 
Pressure, 
Pounds. 

Two-Stage 
Compression, 
D.  H.  P. 

Four-Stage 
Compression, 
D   H.  P. 

10 

3.60 

60 

11.70 

10.80 

15 

5.03 

80 

13.70 

12.50 

20 

6.28 

100 

15.40 

14.20 

25 

7.42 

200 

21.20 

18.75 

30 

8.47 

300 

24.50 

21.80 

35 

9.42 

400 

27.70 

24.00 

40 

10.30 

500 

29.75 

25.90 

45 

11.14 

600 

31.70 

27.50 

50 

11.90 

700 

33.50 

28.90 

55 

12.67 

800 

34.90 

30.00 

60 

13.41 

900 

36.30 

31.00 

70 

14.72 

1000 

37.80 

31.80 

80 

15.94 

1200 

39.70 

33.30 

90 

17.06 

1600 

43.00 

35.65 

100 

18.15 

2000 

45.50 

37.80 

2500 

39.06 

3000 

40.15 

D.  H.  P.,  delivered  horse-power  at  compressor  cylinder. 

Capacity  of  Air  Compressors. 

To  ascertain  the  capacity  of  an  air  compressor  in  cubic 
feet  of  free  air  per  minute,  the  common  practice  is  to 
multiply  the  area  of  the  intake  cylinder  by  the  feet  of 
piston  travel  per  minute.  The  free  air  capacity  of  the 
compressor  divided  by  the  number  of  atmospheres  will 
give  the  volume  of  compressed  air  per  minute.  To 
ascertain  the  number  of  atmospheres  at  any  given  press- 
ure, add  14.7  Ibs.  to  the  gauge  pressure,  divide  this  sum 
by  14.7  and  the  result  will  be  the  number  of  atmospheres. 

The  above  method  of  calculation,  however,  is  only 
theoretical  and  these  results  are  never  obtained  in  actual 
practice  even  with  compressors  of  the  very  best  design. 


NATIONAL  TUBE  COMPANY. 


Allowances  should  be  made  for  losses  of  various  kinds, 
the  principal  loss  being  due  to  clearance  spaces,  but  in 
machines  of  poor  design  and  construction  other  consider- 
able losses  occur  through  imperfect  cooling,  leakages  past 
the  piston  and  through  the  discharge  valves,  insufficient 
area  and  improper  working  of  inlet  valves,  etc.  We 
have  seen  compressors  where  the  total  loss  was  fully  25 
to  30  per  cent.,  whereas,  3  to  10  per  cent,  should  be  the 
maximum — according  to  the  size — in  compressors  of 
proper  design  and  construction. 


"Weights  of  Air ,  Vapor  of  Water,  and  Saturated  Mixtures 
of  Air  and  Vapor  at  Different  Temperatures,  under  the 
Ordinary  Atmospheric  Pressure  of  29.92  inches  of  Mercury. 


.0776 
.0761 
.0747 


.0707 


MIXTURES  OF  AIR  SATURATED  WITH  VAPOR 


.044 

.074 

.118 

.181 

.267 

.388 

.556 

.785 

1.092 

1.501 

2.036 

2.731 

3.621 

4.753 

6.165 

7.930 

10.099 

12.758 

15.960 


24.450 


29.877 
29.849 


29.740 
29.654 
29.533 
29.365 
29.136 


28.420 
27.885 
27.190 
26.300 
25.169 
23.756 
21.991 
19.822 
17.163 
13.961 
10.093 
5.471 
0.000 


Weight  of  Cubic  Foot 

of  the  Mixture  of 

Air  and  Vapor. 


.0659 
.0631 


.000202 
.000304 


.086379 
.084130 


.080504 


.077227 
.075581 
.073921 
.072267 
.070717 


.067046 
.065042 
.063039 
.060873 
.058416 
.055715 


.049336 
.045642 
.041445 


.00092 
.00155 
.00245 
.00379 
.00561 
.00819 
.01179 
.01680 
.02361 
.03289 
.04547 
.06253 
.08584 
.11771 
.16170 
.22465 
.31713 
.46338 
.71300 
1.22643 


182                      NATIONAL  TUBE  COMPANY. 

FLOW  OF  AIR  THROUGH  AN  ORIFICE  FROM  A 
RESERVOIR  INTO  THE  ATMOSPHERE, 
In  Cubic  Feet  of  Free  Air  per  Minute  for  Varying  Diameters 
of  Orifice  and  Gauge  Pressures* 

Diam.  of  Orifice,! 
Inches. 

Receiver  Gauge  Pressure. 

2 
Ibs. 

5 
Ibs. 

10 
Ibs. 

15 
Ibs. 

20 
Ibs. 

25 
Ibs. 

30 
Ibs. 

35 
Ibs. 

40 
Ibs. 

1 
2 

0.038 
0.153 
0.647 
2.435 
9.74 
21.95 
39. 
61. 
87.6 
119.5 
156. 
242. 
350. 
625. 

0.060 
0.242 
0.965 
3.86 
15.4 
34.6 
61.6 
96.5 
133. 
189. 
247. 
384. 
550. 
985. 

0.084 
0.342 
1.36 
5.45 
21.8 
49. 
87. 
136. 
196. 
267. 
350. 
543. 
780. 

0.103 
0.418 
1.67 
6.65 
26.7 
60. 
107. 
167. 
240. 
326. 
427. 
665. 
960. 

0.119 
0.485 
1.93 

so!s 

69. 
123. 
193. 
277. 
378. 
494. 
770. 

0.133 
0.54 
2.16 
8.6 
34.5 
77. 
138. 
216. 
310. 
422. 
550. 
860. 

0.156 
0.632 
2.52 
10. 
40. 
90. 
161. 
252. 
362. 
493. 
645. 
1000. 

0.173 
0.71 
2.80 
11.2 
44.7 
100. 
179. 
280. 
400. 
550. 
715. 

0.19 
0.77 
3.07 
12.3 
49. 
110. 
196. 
307. 
442. 
601. 
785. 

45 
Ibs. 

50 
Ibs. 

60 
Ibs. 

70 
Ibs. 

80 
Ibs. 

90 
Ibs. 

100 
Ibs. 

125 
Ibs. 

150 
Ibs.  , 

1 

0.208 
0.843 
3.36 
13.4 
53.8 
121. 
215. 
336. 
482. 
658. 
860. 

0.225 
0.914 
3.64 
14.50 
58.2 
130. 
232. 
364. 
522. 
710. 
930. 

0.26 
1.05 
4.2 
16.8 
67. 
151. 
268. 
420. 
604. 
622. 

0.295 
1.19 
4.76 
19.0 
76. 
171. 
304. 
476. 
685. 
930. 

0.33 
1.33 
5.32 

21.2 
85. 
191. 
340. 
532. 
765. 
1004. 

0.364 
1.47 
5.87 
23.50 
94. 
211. 
376. 
587. 
843. 

0.40 
1.61 
6.45 
25.8 
103. 
231. 
412. 
645. 
925. 

0.486 
1.97 
7.85 
31.4 
125. 
282. 
502. 
785. 

0.57 
2.33 
9.25 
37.2 
148. 
334. 
596. 
925. 

The  above  table  was  computed  with  the  aid  of  Fliegner's  equa- 
tions and  have  given  results  that  approximate  very  closely  to  the 
conditions  of  actual  practice.    These  equations  are  : 

Yorp^Zpa,    G=  0.530  F  ^J_; 

A>s/a,    £=1.060  pJ&yf&Li  in  which 

G  =  flow  of  air  through  the  orifice  in  Ibs.  per  sec.,  F=  area  of  orifice 
•in  square  inches,  pi  =  pressure  in  reservoir  in  Ibs.  per  sq.  in.,  pa  = 
pressure  of  atmosphere,  7\  =  absolute  temperature,  Fahrenheit,  of 
air  in  reservoir. 

! 

NATIONAL  TUBE  COMPANY. 


FLOW  OF  AIR  THROUGH  PIPES.* 

The  following  new  and  original  tables  are  based  upon 
D'Arcy's  formula  adapted  to  the  flow  of  elastic  fluids, 
namely  : 


Discharge  in  cubic  )  =  ^ 


feet  per  minute     J          r         /  X  W-L 

As  it  is  most  convenient  in  the  case  of  compressed  air 
installations  to  deal  with  its  equivalent  volume  of  free 
air,  i.  e.,  air  at  atmospheric  pressure,  these  tables  have 
been  specially  calculated  with  this  end  in  view. 

Table  L  Gives  the  theoretical  volume  of  equivalent 
free  air  in  cubic  feet  that  will  flow  per  minute 
at  various  pressures  through  straight  pipes  of 
various  diameters,  each  100  feet  long,  no  re- 
duction of  the  final  pressure  being  allowed 
for. 

The  formula  by  which  it  is  calculated  is  : 

Theoretical  discharge  )  c  V  d*        /i 

of  free  air  \~  10        ^ 

Table  II.  Is  a  table  of  multipliers  to  be  used  in  connec- 
tion with  FI,  as  found  by  Table  I.,  by 
which  may  be  obtained  the  theoretical  dis- 
charge of  equivalent  free  air  from  pipes  of 
various  lengths  up  to  60,000  feet.  It  is 
calculated  from 

Multiplier  for 
length  of  pipe 

*Copyright  1899,  by  the  Ingersoll-Sergeant  Drill  Co.,  New  York, 
and  is  reprinted,  by  permission,  from  their  catalogue  of  air 
compressors. 


184  NATIONAL  TUBE  COMPANY. 

Table  HI.  Is  a  table  of  Multipliers  to  be  used  in  con- 
nection with  Ft  and  M\  as  found  by  Tables  I. 
and  II. ,  to  obtain  the  real  volume  of  discharge 
of  equivalent  free  air,  for  reductions  of  the 
terminal  pressure  varying  from  1  to  50  pounds. 
It  is  calculated  from 

Multiplier  for )  f%  

real  discharge  j  f^ 

The  notation  used  in  above  formulas  is 

d— actual  diameter  of  pipe  in  inches. 

/^length  of  pipe  in  feet. 

c=o.  co-efficient,  (D'Arcy's)  varying  with  the  diameter 
of  the  pipe. 

z£/1=density  of  the  air  at  initial  gauge  pressure. 

p±  and  p2~imtial  and  terminal  gauge  pressures. 

/!  and/2=factors  to  reduce  compressed  air  at  initial 
and  terminal  pressures  pt  and.p2  to  their  corresponding 
volumes  of  free  air. 

Tables  are  also  added  showing  the  increase  in  the 
length  of  pipe  to  be  allowed  for  on  account  of  the  fric- 
tion caused  by  globe  valves,  elbows  and  tees. 

Several  examples  are  worked  out  to  show  the  method 
of  using  the  tables  for  the  solution  of  problems  likely 
to  be  met  with  by  the  Engineer. 


NATIONAL  TUBE  COMPANY. 


185 


« 


o*  o 

O5  O  O  -r-c  O 


*OgCOg7-.-OOOTTf.^-T 


HI 

o>  -S 


il 

aj 

w| 

tt  £ 


llii 


Ti'>0*0<Ot>t-OOC30QOCT>0>OrHOtM«Ot:.g<MOO; 


CD  10  CO 


TH  O  O»  CO  OJ  Oi  1-1  00  SO  1-1  0  1-1  T-C  CO  C«  ^  1 

" 


t>  e»  oo  TH  eo  ec  » <»  t-  o 

' 


186                     NATIONAL  TUBE  COMPANY. 

TABLE  IL   MULTIPLIERS  FOR  LENGTH  OF  PIPE. 

Length, 

Multipler 

Length, 

Multipler 

feet. 

Mi. 

feet. 

MX, 

100 

1.0 

6000 

0.129 

200 

0.707 

7000 

0.119 

300 

0.577 

8000 

0.112 

400 

0.500 

9000 

0.105 

500 

0.447 

10000 

0.100 

600 

0.408 

12000 

0.0912 

750 

0.365 

15000 

0.0817 

1000 

0.316 

20000 

0.0707 

1250 

0.283 

25000 

0.0632 

1500 

0.258 

30000 

0.0577 

2000 

0.224 

35000 

0.0534 

2500 

0.200 

40000 

0.0500 

3000 

0.183 

45000 

0.0471 

3500 

0.169 

50000 

0.0447 

4000 

0.158 

55000 

0.0426 

5000 

0.141 

60000 

0.0408 

NATIONAL  TUBE  COMPANY. 


n4 


i 

i? 
§ 

8 
8 

81 

eo"  eo"  co  eo"  eo"  eo"  co"  eo" 
eo  eo  co  co'  co'  eo'  eo  co'  co'  eo"  eo"  co  eo  co  eo  eo  co  eo  co  eo  co  eo  eo 

s§ 

53 

e*d 

si  si  si  si  si  si  si  si  si  si  si  si  si 

l~  I   si  si  si  si  si  si  si  si  si  si  si  si  si  si  oi  si  si  si  si  si  si  si  si  si  si  a* 
50    si  si  st  si  si  si  si  si  si  si  si  si  si  si  si  si  si  si  si  si  si  si  si  si  si  si  si  st 

o  |  gsg§8gSq2SSSS^?3S8S5353§ISS8|§IS! 

co 

l_  d  d  o  o  d  o'  o'  o  d  o  o  o  d  d  d  o  o  o  o  o  o  d  o  d  o  o 

I 


NATIONAL  TUBE  COMPANY. 


The  formulas  by  which  these  tables  have  been  calcu- 
lated  show  that  the  following  factors  enter  into  their 
composition  : 

The  diameter  of  the  pipe  ........  =d. 

The  length  of  the  pipe  ..........  =/. 

The  initial  and  final  pressures,    [     ,       , 

or  the  reduction  of  pressure  i       l      2 
The     equivalent    free    air  dis- 
charged .  .  .  .  ................  —F. 

It  being  often  required  to  find  any  one  of  these  factors 
when  the  others  are  known,  the  following  examples  are 
given  to  show  the  method  of  procedure  in  each  case. 

The  simple  statement  of  the  formula,  adapted  to  the 
tables  becomes 


Free  ai 

and  by  this  all  problems  involving  any  of  the  above  fac- 
tors may  be  solved,  as  shown  in  the  examples. 

EXAMPLE  1.  —  To  find  the  volume  of  free  air  dis- 

charged. 

BXAMPI^E  2.  —  To  find  the  reduction  of  pressure. 
'  '  3.  —  To  find  a  suitable  diameter  of  pipe. 
"  4.  —  To  find  the  length  of  pipe  which 

may  be  used. 

Example  I«  —  Given  a  3-inch  pipe,    10,000   feet  long, 
initial  pressure  1,100  Ibs.,  terminal  pressure  1,050  Ibs.; 
to  find  the  volume   of    equivalent   free  air  discharged. 
By  Table      I.  —  Under  3"  pipe  and  opposite  1,100 

Ibs.  we  find  7^=2,906. 

By  Table    II.—  For  10,000  feet  of  pipe,  Af±~Q.l. 
"       "      III.  —  Under     50     Ibs.    reduction    and 

opposite  1,100  Ibs.,  J/r=6.75. 
Then  as  shown 

^=^tX^iX^r  =  2,906x0.1X6.75  =  l,961  cubic  feet 
free  air. 


NATIONAL  TUBE  COMPANY.  189 

Example  2. — Given  a  4-inch  pipe,  600  feet  long,  initial 
pressure  60  Ibs.,  required  to  discharge  1,200  cubic  feet 
free  air.  What  will  be  the  reduction  of  pressure  and  the 
terminal  pressure  ? 

By  Table    I. — Under  4"  pipe  and  opposite  60  Ibs. , 

we  find  7^=1,535. 
By  Table  II.— For  600  feet,  ^=0.408. 

Given  F=1,2QO. 
By  transposing  the  formula 

F  1,200 

Mr  = = =  1.9. 

ft  X  MI      1,535X0.408 

Now  by  Table  III.,  opposite  60  Ibs.  pressure,  and 
under  4  Ibs.  reduction,  we  find  MT—1.8Q,  so  that  the 
terminal  pressure  will  be  slightly  less  than  60—4=56 
pounds. 

Example  3. — It  is  required  to  discharge  1000  cubic  feet 
of  free  air  from  a  pipe  2,500  feet  long.  The  initial  pres- 
sure is  100  Ibs.  and  the  terminal  pressure  must  not  be 
less  than  90  Ibs.  What  diameter  of  pipe  should  be 
used? 

Here  we  have  given  /^=1000. 

By  Table    II ^=0.200  for  2,500  feet. 

"      "      III Mr=  2.88  for  p±  =  100  Ibs., 

and  A=90  Ibs. 
By  transposing  the  formula  we  get 

F  1,000 

Ft= = =  1,736. 

Ml^Mr       0.200X2.88 

By  Table  I.  looking  along  the  line  of  100  Ibs.  pressure 
we  see  that  the  value  of  Ft  for  a  3}^-inch  pipe  is  1,370, 
and  for  a  4-inch  pipe  1,904,  so  that  this  latter  size  of 
pipe  would  have  to  be  used. 

Example  4, — It  is  required  to  transmit  4,000  cubic  feet 
of  free  air  through  a  6-inch  pipe,  the  initial  pressure 
being  200  Ibs.  How  far  can  it  be  carried  with  a  reduc- 
tion of  pressure  of  10  Ibs.  ? 


190  NATIONAL  TUBE  COMPANY. 

Here  we  have  given  7^=4,000. 

By  Table      I .Ft=7,489  for  200  Ibs.  pressure 

and  6"  pipe. 
By  Table  III Mr=3M  for  200  Ibs.  pressure 

and  10  Ibs.  reduction . 
Then  by  transposing  the  formula : 

F  4,000 

MI- = =0. 177 . 

FtxMr    7,489x3.01 

Now  by  Table  II.  we  see  that  this  is  an  intermediate 
value  of  Mi  between  3000  and  3500  feet,  so  that  the  dis- 
tance sought  is  approximately  3250  feet. 


GLOBE  VALVES,  TEES  AND  ELBOWS. 

The  reduction  of  pressure  produced  by  globe  valves  is 
the  same  as  that  caused  by  the  following  additional 
lengths  of  straight  pipe,  as  calculated  by  the  formula  : 

114  X  diameter  of  pipe 

Additional  length  of  pipe= 

l-f(3.6-f-diameter) 

Diameter  of  pipe.  )      1    lj   2   2j-   3   3j    4    5    6    inches. 
Addition'l length,  j      2    4    7    10  13  16  20  28  36    feet. 

7    8  10  12   15    18    20    22    24  ins. 

44  53  70  88  115  143  162  181  200   ft. 

The  reduction  of  pressure  produced  by  elbows  and 
tees  is  equal  to  f  of  that  caused  by  globe  valves. 

These  additional  lengths  of  pipe  for  globe  valves, 
elbows  and  tees  must  be  added  in  each  case  to  the  actual 
lengths  of  straight  pipe.  Thus,  a  6-inch  pipe,  500  feet 
long,  with  one  globe  valve,  2  elbows  and  three  tees, 
would  be  equivalent  to  a  straight  pipe  500+36-f  (2x24) 
+(3X24)=656  feet  long,  and 'this  is  the  length  which 
must  be  used  in  the  tables  as  the  value  of  MI. 


NATIONAL  TUBE  COMPANY.  191 


GENERAL  EXAMPLE* 

How  much  free  air  will  a  6-inch  pipe,  8,000  feet  long, 
discharge  under  the  following  conditions,  namely : 
Initial  pressure  150  Ibs.,  terminal  pressure  135  Ibs.,  with 
2  globe  valves,  3  elbows  and  1  tee  ? 

The  equivalent  length  of  straight  pipe  must  first  be 
found  as  follows  : 

8,000-f  (2 X36)+ (3x24)+24=8, 168  feet. 
Now  we  have 
By  Table  I.,  /^t=6,558  for  6  inch  pipe  and  150  Ibs. 

pressure. 
By  Table  II.,   ^/i=0.112  for  8000  feet,  making  by 

interpolation  say  0.110  for  8,168  feet. 
By  Table  III.,   Mr=3A2  forlSO  Ibs.  pressure  and 
14  Ibs.  reduction,  and  3.61  for  150  Ibs.  pressure 
and  16  Ibs.  reduction,  so  that  by  interpolation 
Mr  would  be  3.51  for  15  Ibs.  reduction  of  pres- 
sure. 

Then  by  the  formula  : 
Free  air  discharged =F=Ft xMiXMT. 
^6,558X0.11X3.51. 
=2,532  cubic  feet  equivalent 
free  air  per  minute. 

FORMULA  FOR  FLOW  OF  AIR  ESf  PIPES. 

Mr.  Richards,  in  Am.  Mack.,  Dec.  27,  1894,  published 
a  new  formula,  viz. : 

V*L 

£= 


10,000^B«'  L  JS* 


10,000/!> 

in  which  V=  actual  volume  of  compressed  air  delivered, 
in  cubic  feet  per  minute  (not  the  volume  of  free  air,  as 


NATIONAL  TUBE  COMPANY. 


in  the  other  formula),  Z,=length  of  pipe  in  feet,  d—  in- 
ternal diameter  of  pipe  in  inches,  p  —  head  or  additional 
pressure  in  pounds  per  square  inch  required  to  maintain 
the  flow,  and  a  is  a  coefficient  varying  with  the  diameter 
of  the  pipe.  Its  value  for  different  nominal  diameters  of 
wrought-iron  pipe  is  given  by  Mr.  Richards  as  follows  : 


Diam.  , 

Value 

Diam., 

Value 

Diam., 

Value 

Inches. 

of  a. 

Inches. 

of  a. 

Inches. 

of  a. 

1 

.35 

3^ 

.79 

12 

1.26 

IM 

.44 

4 

.84 

16 

1.34 

IK 

.50 

5 

.93 

20 

1.4 

a 

.56 

6 

1. 

24 

1.45 

2^ 

.65 

8 

1.125 

3 

.73 

10 

1.2 

The  following  values  of  the  fifth  power  of  d  and  of  dsa 
are  given  by  Mr.  Richards  to  facilitate  calculations  : 


Fifth  Powers  of  d. 

Value  of  dsa. 

1"  ....      1 

5" 
6" 
8" 
10" 
12" 
16" 
20" 

3,125 
7,776 
32,768 
100,000 
248,&32 
.  1,048,576 
.  .  3,200,000 
.  .  7,962,624 

1"... 

2"  .  .  '. 

$':. 

8H"  •• 

.35 
1.34 
3.80 
18.08 
63.47 
177.4 
413.2 
.  860.2 

5"...    2,918.75 
6'...         7,776 
8"..  i        36,864 
10"  ...      120,000 
12"...      313,528 
16"...  1,405,091 
20"...  4,480,000 
24"...  11,  545,805 

2"..!' 

..      3.05 

..      7.59 
32 

g 

£•:: 

..    97.65 
..  243 
..  525 
.     1024 

GAS. 


a 
^ 


NATIONAL  TUBE  COMPANY. 


FLOW  OF  GAS  IN  PIPES. 

If  d  =  diameter  of  pipe  in  inches  ;  Q  =  quantity  of  gas 
delivered  in  cu.  ft.  per  hour  ;  /  =  length  of  pipe  in  yards  ; 
h  =  pressure  in  inches  of  water  column  ;  s  ~  specific 
gravity  of  the  gas,  air  being  one  ;  then 


Q  =  1000 


Q=l3Wd*A/?^, 

r        Si 


(Moles  worth). 


(King's  Treatise  on  Coal  Gas.) 


Q 


'=1290  y- 


>(J-  P<  Gm>Am-  Gas-light  Jour.,  1894). 


Mr.  Gill's  formula  is  said  to  be  based  on  experimental 
data,  and  to  make  allowance  for  obstructions  by  tar,  etc., 
that  tend  to  check  the  flow  of  gas  through  the  pipe. 

An  experiment  made  by  Mr.  Klegg,  in  London,  on  a 
4  inch  pipe,  6  miles  long,  gave  a  discharge  that  cor- 
responds very  closely  with  that  computed  by  the  use  of 
Molesworth's  formula. 

Maximum  Supply  of  Gas  through  Pipes  in  cu.  ft.  per  Hour, 
Specific  Gravity  being  0.45.    Formula  Q=  tOOO|/  d  *h  +  si. 

(MOLESWORTH.) 
LENGTH  OF  PIPE  =  10  YARDS. 


Diameter  of 
Pipe 
in  Inches. 

Pressure  by  the  Water-gauge  in  Inches. 

0..1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

34 
70 
192 
394 
689 
1082 
2231 

0.8 

0.9 

1.0 

1  4 
2 

13 

26 
73 
149 
260 
411 
843 

18 
37 
103 
211 
368 
581 
1192 

22 
46 
126 
258 
451 
711 
1460 

26 
53 

145 
298 
521 
821 
1686 

29 
59 

162 
333 
582 
918 
1886 

31 

64 
187 
365 
638 
1006 
2066 

36 
74 
205 
422 
737 
1162 
2385 

38 
79 
218 
447 
781 
1232 
2530 

41 
83 
230 
471 
823 
1299 
2667 

NATIONAL  TUBE  COMPANY. 


Maximum  Supply  of  Gas  through  Pipes,  etc.— (CONTINUED.) 
LENGTH  OF  PIPE _=  100  YARDS.        


Pressure  by  the  Water-gauge  in  Inches. 


735  1039  1270  1470 
1080 
1508  2133  2613  301^ 


0.5 

19 

51 
105 
184 
290 
596 
1042 
1643 
2416 
3373 


129 
225 
356 
730 
1276 
2012 
2958 
4131. 


1.0 


26 
73 
149 
260 
411 
843 
1473 


3416  3820  4184 
4770  5333  5842 


581 
1193 


42 
115 
236 

412 
649 


LENGTH  OF  PIPE  =  1000  YARDS. 


Diameter  of 
Pipe 
in  Inches. 

Pressure  by  the  Water-gauge  in  Inches. 

0.5 

0.75 

41 
113 
231 
403 
636 
1306 
2282 
3600 

1.0 

47 
130 
267 
466 
735 
1508 
2635 
4157 

1.5 

2.0 

2.5 

3.0 

1* 
y 

4 
5 
6 

33 
92 

189 
329 
520 
1067 
1863 
2939 

58 
159 
327 
571 
900 
1847 
3227 
5091 

67 
184 
377 
659 
1039 
2133 
3727 
5879 

75 
205 
422 
737 
1162 
2385 
4167 
6573 

82 
226 
462 
807 
1273 
2613 
4564 
7200 

LENGTH  OF  PIPE  =  5000  YARDS. 


s  J 

u* 

5  •* 

Pressure  by  the  Water-gauge  in  Inches. 

1.0 

1.5 

2.0 

2.5 

3.0 

2 
3 

4 
5 
6 
7 
8 
9 
10 
12 

119 
329 
675 
1179 
1859 
2733 
3816 
5123 
6667 
10516 

146 

402 
826 
1443 

2277 
3347 
4674 
6274 
8165 
12880 

169 
465 
955 
1667 
2629 
3865 
5397 
7245 
9428 
14872 

189 
520 
1067 
1863 
2939 
4321 
6034 
8100 
10541 
16628 

207 
569 
1168 
2041 
3220 
4734 
6610 
8873 
11547 
18215 

Where  there  is  apt  to  be  trouble  from  frost  no  pipe  less  than  % 
inch  should  be  used,  and  in  extremely  cold  climates  the  smallest 
size  should  not  be  less  than  one  inch. 

To  provide  for  the  resistance  due  to  bends,  one  rule  is  to  allow  a 
pressure  of  0.204  inch  of  water  column  for  each  right  angled  elbow. 


1% 

NATIONAL  TUBE  COMPANY. 

Services  for  Burners* 

The  following  table  is  the  standard  of  the  principal  gas 
works.     It  governs  the  size  of  pipe  used  by  gas  fitters 
for  consumers,  and  will  be  found  of  value.    Every  service 

should  have  a  T  so  placed  as  to  permit  of  easily  clearing 
the  service  pipe  should  any  obstruction  occur  in  it. 

Size 

Threads 

Weight 

Length 

Number  of 

of  Pipe. 

per  Inch. 

per  Foot. 

allowed. 

Burners. 

Feet. 

I/ 

27 

.243 

2 

1 

M^ 

18 

.422 

6 

1 

a/ 

14 

.561 

20 

3 

l/ 

14 

-.845 

30 

6 

3£ 

UK 

1.126 

50 

20 

1 

UK 

1.670 

70 

35 

l/€ 

UK 

2.258 

100 

60 

IK 

2.694 

150 

100 

2 

8  2 

3.367 

200 

200 

%y 

8 

5.773 

300 

300 

3 

8 

7.547 

450 

450 

4 

8 

10.728 

600 

750 

TABLE  OF  AQUEOUS  VAPOR 

Contained  in  1000  Cubic  Feet  of  Gas  at  Indicated 

Temperature 

Temp. 
Degrees 

Volume, 
Aqueous 
Vapor. 

Temp 
Degrees 

Volume, 
Aqueous 
Vapor. 

Temp. 
Degrees 

Volume, 
Aqueous 
Vapor. 

40 

9.33 

54 

15.33 

68 

24.06 

41 

9.73 

55 

15.  8( 

> 

69 

24.83 

42 

10.13 

56 

16.40 

70 

25.66 

43 

10.53 

57 

16.93 

71 

26.53 

44    - 

10.93 

58 

17.53 

72 

27.40 

45 

11.33 

59 

18.10 

73 

28.30 

46 

11.73 

60 

18.  6( 

1 

74 

29.23 

47 

12.13 

61 

19.23 

75 

30.20 

48 

12.53 

62 

19.  8( 

) 

76 

31.20 

49 

12.93 

63 

20.50 

77 

32.20 

50 

13.33 

64 

21.20 

78 

33.23 

51 

13.80 

65 

21.90 

79 

34.23 

52 

14.26 

66 

22.60 

80 

35.33 

53 

14.80 

67 

23.  3( 

) 

81 

36.43 

^—                                              —  M  s 

NATIONAL  TUBE  COMPANY.         197 
1 

TABLE  OF  THE  WEIGHTS  OF  GAS-HOLDERS. 

1  In  Pounds  for  every  One-tenth  of  an  Inch  maximum 

Pressure,  and  for  Diameter  from  20  to  200  Feet. 

i 

•§°S 

•£ 

.o'og 

|j 

oooJ 

<~% 

,0*0  <u" 

•ofe 

"5  S 

*o^ 

.Sci 

•gfc 

ui'S  3 

w'S  w 

fc.S 

£  G  0) 

•".S 

.O  C  jg 

^.S 

rQ  d  W 

"a  Y£ 

i»  i 

fl'tfi 

*j  £ 

'S'Yfi 

0)  a) 

.sif&i 

62 

62 

,S  ou 

^"o 

rG  OO 

rt'S 

rG  QO 

nj  o 

rC  O  0 

1 

bOgS 
||g 

°3 

0 

111 

I 

|ll 

b1 

O 

i>Sg 

20 

164 

53 

1149 

86 

3026 

119 

5793 

21 

181 

54 

1193 

87 

3097 

120 

5891 

22 

198 

55 

1238 

88 

3168 

121 

5990 

23 

217 

56 

1283 

89 

3241 

122 

6089 

24 

236 

57 

1329 

90 

3314 

123 

6189 

25 

256 

58 

1376 

91 

3388 

124 

6290 

26 

277 

59 

1424 

92 

3463 

125 

6392 

27 

298 

60 

1473 

93 

3538 

126 

6495 

28 

321 

61 

1522 

94 

3615 

127 

6598 

29 

344 

62 

1573 

95 

3692 

128 

6703 

30 

368 

63 

1624 

96 

3770 

129 

6808 

31 

393 

64 

1676 

97 

3849 

130 

6914 

32 

419 

65 

1729 

98 

3929 

131 

7021 

33 

446 

66 

1782 

99 

4010 

132 

7128 

34 

473 

67 

1837 

100 

4091 

133 

7237 

35 

501 

68 

1892 

101 

4173 

134 

7346 

36 

530 

69 

1948 

102 

4256 

135 

7456 

37 

560 

70 

2005 

103 

4340 

136 

7567 

38 

591 

71 

2062 

104 

4425 

137 

7678 

39 

622 

72 

2121 

105 

4510 

138 

7791 

40 

655 

73 

2180 

106 

4597 

139 

7904 

41 

688 

74 

2240 

107 

4684 

140 

8018 

42 

723 

75 

2301 

108 

4772 

141 

8133 

43 

757 

76 

2363 

109 

4861 

142 

8249 

44 

792 

-77 

2426 

110 

4950 

143 

8366 

45 

828 

78 

2489 

111 

5041. 

144 

8483 

46 

866 

79 

2553 

112 

5132 

145 

8601 

47 

904 

80 

2618 

113 

5224 

146 

8720 

48 

943 

81 

2684 

114 

5317 

147 

8840 

149 

982 

82 

2751 

115 

5410 

148 

8961 

50 

1023 

83 

2818 

116 

5505 

149 

9083 

51 

1064 

84 

2887 

117 

5600 

150 

9205 

52 

1106 

85 

2956 

118 

5696 

200 

16364 

«- 

NATIONAL  TUBE  COMPANY. 


Example. — Find  the  weight  of  a  gas-holder  80  feet  in 
diameter,  the  maximum  pressure  being  3.2  inches  water 
column,  or  32/10ths. 

In  preceding  table,  opposite  80  in  column  of  diameters 
read  2618,  the  weight  for  l/10th  inch  pressure.  There- 
fore the  weight  required  =  2618  X  32  =  83,776  Ibs. 


IRON  AND  STEEL. 


NATIONAL  TUBE  COMPANY. 


IRON  AND  STEEL. 

Wrought  Iron  is  the  product  of  the  puddling  process. 
It  is  made  in  a  reverberatory  furnace  by  melting  pig 
iron  on  a  hearth  of  iron  oxide,  over  which  passes  a 
reducing  flame  which  causes  the  carbon  to  unite  with 
the  oxide  during  the  mixing  which  the  puddler  gives  it, 
and  further  causes  a  large  portion  of  the  impurities  to 
enter  the  surrounding  slag.  As  the  impurities — carbon, 
manganese,  phosphorus,  sulphur,  silicon — leave  the 
molten  iron,  the  melting  point  rises  so  that  the  iron 
becomes  first  viscous,  then  pasty.  When  it  has  been 
worked  into  a  ball  the  puddler  carries  it,  still  at  a 
welding  heat,  to  the  hammer  or  squeezer  where  the 
greater  part  of  the  slag  which  permeated  it  is  expelled 
from  the  mass.  The  roughly  shapen  slab  is  then  rolled 
into  muck  bar,  which,  when  piled,  rolled  and  re-rolled 
becomes  the  wrought  iron  of  commerce. 

Steel  is  the  malleable  product  of  either  the  cementation 
process,  the  crucible,  the  converter  or  the  open  hearth 
furnace. 

Cementation  is  the  earliest  process  that  we  know  of  for 
making  steel,  and  was  founded  upon  the  fact  that 
wrought  iron  if  packed  in  charcoal  and  heated  to  a  high 
temperature,  while  excluded  from  air,  absorbs  carbon. 
The  process  consisted  in  packing  bars  of  wrought  iron, 
of  about  ^  inch  thickness,  in  charcoal,  and  then  sealing 
up  the  vessel  and  keeping  it  at  a  yellow  heat  until  the 
carbon  had  penetrated  to  the  centres  of  the  bars  and 
converted  them  into  steel.  The  carbon  penetrates  the 
bar  at  the  rate  of  about  }£  inch  in  24  hours,  and  while 
the  point  of  saturation  of  iron  by  carbon  is  about  1.50%, 
yet  the  average  content  of  carbon  by  this  process  in  the 
finished  bars,  is  about  1%  or  lower. 

The  use  of  steel  made  by  this  process  was  always 
limited  because  of  the  fact  that  it  contained  the  old 
seams  and  slag  [marks  which  everywhere  crossed  and 


NATIONAL  TUBE  COMPANY.  201 

recrossed  the  iron,  causing  great  trouble  in  the  manu- 
facture of  cutting  tools.  But  by  melting  this  steel 
(called  also  blister  steel,  because  its  surface  was  covered 
with  blisters)  in  a  covered  crucible,  the  seams  and  fibres 
of  slag  all  disappeared,  and  a  homogeneous  ingot  was  the 
result.  But  this  was  a  long  way  to  a  steel  ingot,  and  the 
pursuit  of  cheapness  gave  rise  to  the  direct  method  of 
melting  iron  in  a  crucible,  made  for  the  purpose,  together 
with  the  requisite  carbon  and  other  ingredients  necessary 
for  imparting  hardness,  toughness,  etc.  The  molten  iron 
absorbs  the  carbon  very  quickly  and  gives  a  product 
which  approaches  closely  the  merit  of  that  produced  by 
the  older  method. 

Up  to  the  middle  of  the  nineteenth  century  these  two 
processes  were  the  principal  ones,  yet  they  were  too 
expensive  for  a  product  of  general  use,  except  for  tools. 

About  1856,  Sir  Henry  Bessemer  completed  his  experi- 
ments and  gave  to  the  world  his  famous  process.  In  this 
process  the  pig  iron  is  melted  and  poured  into  a  bottle 
shaped  vessel.  Air  is  then  blown  into  it  from  the  bottom, 
burning  out,  first  the  silicon,  then  the  manganese  and 
carbon,  (the  first  two  elements  entering  the  slag,  the  last 
one  going  out  of  the  mouth  of  the  converter  as  gas)  but 
not  reducing  either  the  phosphorus  or  sulphur.  When 
the  carbon  is  burned  out — a  fact  recognized  by  the  color 
of  the  flame— the  vessel  contains  practically  pure  wrought 
iron,  which  becomes  steel  on  the  addition  of  sufficient 
carbon  and  manganese  to  give  the  requisite  hardness  and 
toughness  to  the  cast. 

When  the  iron  is  melted  in  a  Converter  which  has  a 
silicon  lining  the  process  is  called  the  Acid  Bessemer, 
and  the  principal  fuel  to  keep  the  bath  liquid  is  silicon. 
If  the  iron  is  high  in  phosphorus  and  melted  in  a  vessel 
lined  with  dolomite  or  magnesite  the  process  is  called  the 
Basic  Bessemer  and  phosphorus  is  the  principal  element 
of  fuel. 

Following  the  introduction  of  Sir  Henry  Bessemer's 
process,  William  Siemans  invented  the  regenerative 


202 NATIONAL  TUBE  COMPANY. 

furnace,  a  furnace  in  which  the  heat  of  the  waste  gases 
passes  through  chambers  checkered  off  with  fire  brick, 
which  so  obstruct  the  passage  of  the  gases  to  the  chimney 
as  to  make  them  give  up  their  heat.  The  air  and  fuel  gas 
entering  the  furnace  is  then  passed  through  this  hot 
checker  work  and  highly  heated,  thus  returning  to  the 
furnace  a  large  part  of  the  heat  carried  out  before  by  the 
gases  passing  to  the  stack.  In  a  furnace  of  similar  con- 
struction Open  Hearth  Steel  is  made.  Pig  iron,  steel 
scrap,  wrought  iron,  and  iron  ore  charged  together,  or 
separately,  (all,  one  or  any  two  of  them)  are  rendered  steet 
by  burning  out  their  impurities  with  an  oxidizing  flame. 
If  the  metal  is  melted  on  a  hearth  lined  with  sand,  the 
carbon,  manganese  and  silicon  are  burned  out  and  the 
sulphur  and  phosphorus  remain  as  before.  This  is  the 
Acid  Open  Hearth  Process.  But  if,  on  the  other  hand, 
the  bottom  is  made  of  dolomite  or  magnesite,  and  lime 
is  added  to  hold  the  phosphorus  in  the  slag  formed  (as  in 
the  case  of  Basic  Bessemer)  the  phosphorus,  silicon,  car- 
bon and  manganese  are  burned  out,  and  sulphur  remains 
as  before.  This  is  the  Basic  Open  Hearth  process. 

We  have,  then,  steel  made  by  the  following  processes: 

1st.     Cementation. 

2d.      Crucible. 

3rd.     Bessemer,  ]  j>     •    f  Converter. 
4th.     Open  Hearth,  j  R^:    [  Furnace. 


Standard  Specifications  for  Special  Open-Hearth  Plate  and 

Rivet  Steel,  as  adopted  by  the  Association  of 

American  Steel  Manufacturers. 

Testing  and  Inspection  (1).  All  tests  and  inspections 
shall  be  made  at  place  of  manufacture  prior  to  shipment. 

Test  Pieces  (2).  The  tensile  strength,  limit  of  elasticity 
and  ductility,  shall  be  determined  from  a  standard  test 


NATIONAL  TUBE  COMPANY  203 

piece  cut  from  the  finished  material.  The  standard 
shape  of  the  test  piece  for  sheared  plates  shall  be  as 
shown  by  the  following  sketch  : 


Piece  to  be  of  same  thickness  as  the  plate. 

On  tests  cut  from  other  material  the  test  piece  may  be 
either  the  same  as  for  plates,  or  it  may  be  planed  or 
turned  parallel  throughout  its  entire  length.  The  elon- 
gation shall  be  measured  on  an  original  length  of  8  inches, 
except  when  the  thickness  of  the  finished  material  is 
5-16  inch  or  less,  in  which  case  the  elongation  shall  be 
measured  in  a  length  equal  to  sixteen  times  the  thickness; 
and  except  in  rounds  of  %  inch  or  less  in  diameter,  in 
which  case  the  elongation  shall  be  measured  in  a  length 
equal  to  eight  times  the  diameter  of  section  tested. 
Four  test  pieces  shall  be  taken  from  each  melt^>f  finished 
material ;  two  for  tension  and  two  for  bending. 

Annealed  Test  Pieces  (3).  Material  which  is  to  be  used 
without  annealing  or  further  treatment  is  to  be  tested  in 
the  condition  in  which  it  conies  from  the  rolls.  When 
material  is  to  be  annealed  or  otherwise  treated  before  use, 
the  specimen  representing  such  material  is  to  be  similarly 
treated  before  testing. 

Marking  (4).  Every  finished  piece  of  steel  shall  be 
stamped  with  the  melt  number.  Rivet  steel  may  be 
shipped  in  bundles  securely  wired  together,  with  the 
melt  number  on  a  metal  tag  attached. 

Finish  (5).  All  plates  shall  be  free  from  surface  de- 
fects and  have  a  workmanlike  finish. 


NATIONAL  TUBE  COMPANY. 


Chemical  Properties  (6). 

Extra   soft  and  [Maximum    Phosphorous,    .04  % 
Fire  Box  Steel.  J          "  Sulphur.  .04  % 

Flange  or  boiler )          "  Phosphorous,  .06  % 

Steel.  J          "  Sulphur,  .04  % 

Boiler    Rivet       )          "  Phosphorous,  .04  % 

Steel.  f          "  Sulphur,  .04  % 

Physical  Properties  (7).  Steel  shall  be  of  four  grades— 
EXTRA  SOFT,  FIRE  Box,  FLANGE  or  BOILER,  and  BOILER 
RIVET  STEEI*. 

Extra  Soft  Steel  (8).  Ultimate  strength,  45,000  to  55,000 
pounds  per  square  inch. 

Elastic  limit,  not  less  than  one-half  the  ultimate 
strength.  Elongation,  28  per  cent. 

Cold  and  Quench  bends,  180  degrees  flat  on  itself, 
without  fracture  on  outside  of  bent  portion. 

Fire  Box  Steel  (9).  Ultimate  strength,  52,000  to  62,000 
pounds  per  square  inch. 

Elastic  limit,  not  less  than  one-half  the  ultimate 
strength.  Elongation  26  per  cent. 

Cold  and  Quench  bends,  180  degrees,  flat  on  itself, 
without  fracture  on  outside  of  bent  portion. 

Flange  or  Boiler  Steel  (10).  Ultimate  strength,  52,000  to 
62,000  pounds  per  square  inch. 

Elastic  fimit,  not  less  than  one-half  the  ultimate 
strength.  Elongation,  25  per  cent. 

Cold  and  Quench  bends,  180  degrees  flat  on  itself, 
without  fracture  on  outside  of  bent  portion. 

Boiler  Rivet  Steel  (11).  Steel  for  boiler  rivets  shall  be 
made  of  the  extra  soft  quality  specified  in  paragraph 
No.  8. 

Variation  When  Ordered  to  Gauge  (12).  For  all  plates 
ordered  to  gauge,  there  will  be  permitted  an  average 
excess  of  weight  over  that  corresponding  to  the  dimen- 
sions on  the  order  equal  in  amount  to  that  specified  in 
the  following  table,  provided  no  plate  shall  be  rejected 
for  light  gauge  measuring  .01"  or  less,  below  the  ordered 
thickness. 


NATIONAL  TUBE  COMPANY. 


Table  of  Allowances  for  Overweight  for  Rectangular 
Plates  J/4  Inch  Thick  and  Heavier. 

NOTE. — The  weight  of  1  cubic  inch  of  rolled  steel  is 
taken  at  0.2833  pounds. 


THICKNESS  OF 

WIDTH  OF  PLATE. 

PLATE. 

Up  to  75  in. 

75  in.  to  100  in. 

Over  100  in. 

Min.... 

10  percent. 

14  percent. 

18  percent. 

8 

12 

16 

% 

7 

10 

13 

T7tf 

6 

8 

10 

» 

5 

7 

9 

M 

4  2 

6  2 

8  2 

Over  % 

&A 

5 

6K 

Table  of  Allowances  for  Overweight  for  Rectangular 
Plates  less  than   J/4  Inch  in  Thickness. 


THICKNESS  OF 
PLATE. 

WIDTH  OF  PLATE. 

Up  to  50  in. 

50  in.  and  above. 

i^  in.  up  to  -fa  in. 
•&                   f3* 

A      "       K  " 

10    per  cent. 

8K        " 

7            " 

15  per  cent. 

12          «« 
10 

Variation  When  Ordered  to  Weight  (13).  Plates  12^  Ibs. 
or  heavier  when  ordered  to  weight,  shall  not  average 
more  variation  than  2^  per  cent. ,  either  above  or  below 
the  theoretical  weight. 

Plates  from  10  to  12^  Ibs.,  when  ordered  to  weight, 
shall  not  average  a  greater  variation  than  the  following  : 

Up  to  75  inches  wide,  2^  per  cent.,  either  above  or 
below  the  theoretical  weight. 

75  inches  and  over,  5  per  cent. ,  either  above  or  below 
the  theoretical  weight. 

Plates  under  10  Ibs.  down  to  5  Ibs.  when  ordered  to 
weight  shall  not  average  more  variation  than  3  per  cent, 
above  or  5  per  cent,  below  the  theoretical  weight. 

Plates  under  5  Ibs.  when  ordered  to  weight  shall  not 
average  more  variation  than  5  per  cent,  either  above 
or  below  the  theoretical  weight. 


NATIONAL  TUBE  COMPANY. 


NATIONAL  TUBE  COMPANY. 


TENACITY  OF  METALS  AT  VARIOUS 
TEMPERATURES. 

Tensile  Strength  of  Iron  and  Steel  at  High  Temperatti res. — 
James  E.  Howard's  tests  (Iron  Age,  April  10,  1890),  shows 
that  the  tensile  strength  of  steel  diminishes  as  the  tem- 
perature increases  from  0°  until  a  minimum  is  reached 
between  200°  and  300°F.,  the  total  decrease  being  about 
4,000  Ibs.  per  square  inch  in  the  softer  steels  and  from 
6,000. to  8,000  Ibs.  in  steels  of  over  80,000  Ibs.  tensile 
strength.  From  this  minimum  point  the  strength  in- 
creases up  to  a  temperature  of  400°  to  650°F. ,  the  maxi- 
mum being  reached  earlier  in  the  harder  steels,  the  in- 
crease amounting  to  from  10,000  to  20,000  Ibs.  per  square 
inch  above  the  minimum  strength  at  from  200°  to  300°. 
From  this  maximum,  the  strength  of  all  the  steels  decreases 
steadily  at  a  rate  approximating  10,000  Ibs.  decrease  per 
100°  increase  of  temperature.  A  strength  of  20,000  Ibs. 
per  square  inch  is  still  shown  by  0.10  C.  steel  at  about 
1000  F.,  and  by  0.60  to  1.00  C.  steel  at  about  1600°  F. 

The  strength  of  wrought  iron  increases  with  tempera- 
ture from  0°  up  to  a  maximum  at  from  400  to  600°  F.,  the 
increase  being  from  8,000  to  10,000  Ibs.  per  square  inch, 
and  then  decreases  steadily  till  a  strength  of  only  6,000 
Ibs.  per  square  inch  is  shown  at  1,500°F. 

Cast  iron  appears  to  maintain  its  strength,  with  a  ten- 
dency to  increase,  until  900°  is  reached,  beyond  which 
temperature  the  strength  gradually  diminishes.  Under 
the  highest  temperatures,  1,500°  to  1,600°  F.,  numerous 
cracks  on  the  cylindrical  surface  of  the  specimen  were 
developed  prior  to  rupture.  It  is  remarkable  that  cast 
iron,  so  much  inferior  in  strength  to  the  steels  at  atmos- 
pheric temperature,  under  the  highest  temperatures  has 
nearly  the  same  strength  the  high-temper  steels  then  have. 

Strength  of  Iron  and  Steel  Boiler-plate  at  High  Tempera- 
tures. (Chas.  Huston,  Jour.  K  I. ,  1877.) 

AVERAGE  OF  THREE  TESTS  OF  EACH. 


Temperature  F 

Charcoal  iron  plate,  tensile  strength,  Ibs. . 

"  "       "      contr.  of  area  % 

Soft  open-hearth  steel,  tensile  strength,  Ibs. 

"     cpntr.  % 

"    Crucible  steel,  tensile  strength,  Ibs... 
"          "  "      contr.  % 


55,366 
26 

54,600 

47 
64,000 


925° 
65,343 

21 
64,350 

33 


21 


NATIONAL  TUBE  COMPANY. 


Strength  of  Wrought  Iron  and  Steel  at  High  Temperatures. 
— (Jour.  F.  /.,  cxii.,  1881,  p.  241.)  Kollmann's  experi- 
ments at  Oberhausen  included  tests  of  the  tensile  strength 
of  iron  and  steel  at  temperatures  ranging  between  70°  and 
2000°  F.  Three  kinds  of  metal  were  tested,  viz.,  fibrous 
iron  having  an  ultimate  tensile  strength  of  52,464  Ibs., 
an  elastic  strength  of  38,280  Ibs.,  and  an  elongation  of 
17.5$;  fine-grained  iron  having  for  the  same  elements 
values  of  56,892  Ibs.,  39,113  Ibs.,  and  20$;  and  Bessemer 
steel  having  values  of  84,826  Ibs.,  55,029  Ibs.,  and  14.5*. 
The  mean  ultimate  tensile  strength  of  each  material  ex- 
pressed in  per  cent,  of  that  at  ordinary  atmospheric  tem- 
perature is  given  in  the  following  table,  the  fifth  column 
of  which  exhibits,  for  purposes  of  comparison,  the  results 
of  experiments  carried  on  by  a  committee  of  the  Frank- 
lin Institute  in  the  years  1832-36. 


Temperature 
Degrees  F. 

Fibrous 
Wrought 
Iron,  p.  c. 

Fine-grained 
Iron, 
per  cent. 

Bessemer 
Steel, 
per  cent. 

Franklin 
Institute, 
per  cent. 

0 

100.0 

100.0 

100.0 

96.0 

100 

100.0 

100.0 

100.0 

102.0 

200 

100.0 

100.0 

100.0 

105.0 

300 

97.0 

100.0 

100.0 

106.0 

400 

95.5 

100.0 

100.0 

106.0 

500 

92.5 

98.5 

98.5 

104.0 

600 

88.5 

95.5 

92.0 

99.5 

700 

81.5 

90.0 

68.0 

92.5 

800 

67.5 

77.5 

44.0 

75.5 

900 

44.5 

51.5 

36.5 

53.5 

1000 

26.0 

36.0 

31.0 

36.0 

1100 

20.0 

30.5 

26.5 

1200 

18.0 

28.0 

22.0 

1300 

16.5 

23.0 

18.0 

1400 

13.5 

19.0 

15.0 

1500 

10.0 

15.5 

12.0 

1600 

7.0 

12.5 

10.0 

1700 

5.5 

10.5 

8.5 

1800 

4.5 

8.5 

7.5 

1900 

3.5 

7.0 

6.5 

2000 

3.5 

5.0 

5.0 

NATIONAL  TUBE  COMPANY.  209 

MECHANICS  OF  MATERIALS  RELATING  TO 
TUBULAR  CONSTRUCTION. 


STRENGTH  OF    MATERIALS. 

A  tensile  stress  is  produced  in  the  walls  of  a  cylindrical 
vessel,  such  as  a  pipe,  tank,  boiler,  etc.  when  it  contains 
a  fluid  such  as  water,  steam  or  air,  under  pressure. 

The  ultimate  or  breaking  strength  of  a  material  is  reached 
when  the  tensile  stress  equals  its  cohesive  force,  in  which 
case  the  material  is  on  the  point  of  being  ruptured. 

The  working  strength  of  a  material  is  that  fraction,  or 
portion,  of  the  ultimate  or  breaking  strength  that  experi- 
ence has  shown  it  is  best  to  use  in  practice,  in  order  to 
guard  against  failure  due  to  unforeseen  causes,  such  as 
defects  and  the  possible  action  of  unknown  forces . 

The  unit  working  strength  of  a  material  is  the  working 
strength  of  one  square  inch  of  cross  section  of  that  ma- 
terial. 

The  factor  of  safety  is  the  factor  or  number  by  which 
the  ultimate  strength  is  divided  in  order  to  obtain  the 
working  strength.  The  proper  factor  to  use  in  any  given 
case  would  depend  upon  the  characteristics  of  the  ma- 
terial and  the  nature  of  the  forces,  whether  quiescent  or 
impulsive. 

In  tubular  construction,  reasonably  free  from  vibration 
and  shock,  a  factor  of  safety  of  from  5  to  6  should  be 
ordinarily  used  for  wrought  iron  and  steel,  and  from  8  to 
10  for  cast  iron.  Where  there  is  uncertainty  as  to  the 
magnitude  and  nature  of  the  forces  acting,  or  where  there 
is  much  vibration  or  shock,  such  as  water  hammer  in 
steam  pipes  or  the  sudden  stoppage  of  flow  in  a  water 
pipe,  these  factors  should  be  increased  to  from  one  and 
one-half  to  three  or  more  times  the  values  given,  depend- 
ing upon  the  severity  of  the  vibration  or  shock. 

It  is  best,  when  possible,  to  compute  the  straining  ac~ 
tions  of  shocks,  as  for  example  the  increase  in  fluid  pres- 


sure in  a  long  water  pipe  when  the  flow  is  more  or  less 
quickly  checked,  in  which  case  they  should  be  added  to 
the  normal  straining  action.  Having  provided  for  these 


abnormal  forces,  the  ordinary  factors  of  safety  should 
then  be  used . 

Stress  and  Strain. — Should  the  fluid  pressure  in  a  cylin- 
drical vessel  be  gradually  increased  from  zero,  it  will  be 


NATIONAL  TUBE  COMPANY. 


observed  that  the  walls  of  the  vessel  will  stretch,  thus  in- 
creasing its  volume.  The  stretch  of  the  material  consti- 
tuting the  walls  is  termed  the  strain  due  to  the  force 
tending  to  tear  the  material  asunder. 

The  molecular  actions  within  the  material  which  oppose 
the  external  forces,  and  which  resist  deformation,  are 
termed  stresses. 

An  elastic  material  when  deformed  by  a  straining  action 
recovers  its  original  form  when  the  straining  action  is 
removed;  as,  for  example,  spring  steel,  ivory,  etc. 

A  plastic  material  when  deformed  does  not  recover  its 
original  form  when  the  straining  action  is  removed;  as, 
for  example,  lead,  putty,  etc. 

Elastic  limit. — Materials  such  as  wrought  iron  and  low 
carbon  steel  are  elastic  under  some  conditions  and  plastic 
under  others.  At  ordinary  atmospheric  temperatures, 
these  materials  may  be  strained  up  to  a  point,  termed  the 
elastic  limit,  without  suffering  any  permanent  deforma- 
tion when  the  straining  action  is  removed. 

Should,  however,  the  elastic  limit  be  exceeded,  the  ma- 
terial will  but  partially  recover  its  original  form  when  the 
straining  action  is  removed,  in  which  case  it  is  said  to 
have  received  a  permanent  deformation  or  set. 

Up  to  the  elastic  limit  the  strain  is  proportional  to  the 
stress,  that  is,  strain  -f-  stress  =  a  constant.  Beyond 
the  elastic  limit  this  constant  becomes  ordinarily  an  in- 
creasing varible. 

The  modulus  of  elasticity  of  a  material  is  obtained  by 
dividing  the  unit  stress  by  the  strain,  for  unit  length. 

Shearing  strength  of  a  material— When  a  cylindrical  ves- 
sel, made  up  from  plates,  connected  together  in  the  usual 
manner  by  riveted  joints,  is  subjected  to  a  fluid  pressure, 
the  adjoining  plates  will  tend  to  separate  by  sliding  one 
upon  the  other,  thus  subjecting  the  material  of  the  rivets 
to  a  shearing  action.  The  ability  of  a  rivet  to  resist  this 
action  is  known  as  its  shearing  strength,  and  the  stress 
created  by  snch  action  is  called  the  shearing  stress . 

Unit  shearing  strength  of  a  material  is  the  shearing 
strength  of  one  square  inch  of  cross -section  of  that  ma- 
terial . 


NATIONAL  TUBE  COMPANY.                      211 

VALUES  OF  I  (Moment  of  Inertia),  AND  S.  (Section 
Modulus),  FOR  USUAL  SECTIONS. 

SECTIONS. 

I 

S 

.<—&-•* 

z_bh3 
12 

bha 
6 

'  ••"*! 

i4P 

_bh3 

Min  — 

36 

24 

*•*•• 

Xd4 

Trd8 

=0.0491  d4 

32 

=0.0982  d3 

,-*..,, 

-r     bh  3  —  b  1  li  1  3 
I  — 

I 
0.5h 

*'EBf 

12 

•-<©- 

1=0.0491  (d4^!4) 

,«(<,,!.•) 

:<  b  -  J'"" 

t     b^.+bn^^-b^' 

Min.=JL 
n 

3 

HH 

T     bh^bjb.!3 

I 

12 

0.5h. 

x  x  Denotes  position  of  neutral  axis. 

Bending  Moments  and  Deflections  of  Beams  under  Various    1 
Systems  of  Loading. 

JF=  total  load. 
/=  length  of  beam. 

7=moment  of  inertia 
.Z?=modulus  of  elasticity. 

(1)    Beam  fixed  at  one  end  and 
loaded  at  the  other. 

mp.  1-  ->• 

(2)    Beam  fixed  at  one  end,  and     \ 
uniformly  loaded. 

Maximum  bending  moment  at 
point  of  support  =  Wl. 
Maximum  shear  at  point  of  sup- 
Deflection  =3^-7 

Maximum  bending  moment  at     \ 
point  of  support^— 
Maximum   shear   at    point    of     \ 

(3)    Beam   supported   at    both 
ends,  single  load  in  the  middle 

'<                /                >' 

(4)    Beam   supported   at    both 
ends  and  uniformly  loaded. 

W  

1       ®        d 

Maximum  bending  moment  at 
middle  of  beam=-j- 
Maximum  shear  at   points   of 

Deflection=     „, 

^H|f         ....      .        ™j||b 

Maximum  bending  moment  at 
middle  of  beam  =—  g— 
Maximum  shear   at    points   of 

(5)    Beams  supported  at   both 
ends,    single    unsymmetncal 
load. 

(6)    Beam  fixed  at  both   ends 
and  uniformly  loaded. 

rtr 

I||L.  ^  1  _a  

Maximum  bending  moment  un- 

Maximum   shear  :   at    support 

Wb 
near  a—  -y-;  at  other  support 

_Wa 
Maximum  deflection 

SSssT                 /                  ^^^ 

Maximum  bending  moment  at 

Wl 

point  of  support=  —r^- 

Maximum   shear  at    points  of 
Wl* 

«*// 

;  4 

NATIONAL  TUBE  COMPANY. 


213 


DEFLECTION  AND  STRENGTH  OF  PIPES  TO 
RESIST  BENDING  ACTION. 

The  bending  moment  of  a  force  is 
obtained  by  multiplying  the  force, 
P,  in  pounds,  by  the  lever  arm,  /, 
in  inches,  with  which  it  acts.  Thus 
in  the  case  of  a  trolley  pole  the 
bending  moment  at  the  ground, 
G,  is 

M=P  1,  and  at  Gl  is  M1=P11. 
The  deflection  of  a  pipe  or  tube 
when  loaded  transversely,  that  is, 
so  as  to   subject  it   to  a  bending 

moment,  is  the  deformation  in  inches  produced  by  the 
given  loading,  and  is  due,  of  course,  to  the  elasticity  of 
the  materials  constituting  it.  In  case  of  a  trolley  pole 
the  greatest  deformation  will  be  at  the  extreme  top  of 
the  pole. 

For  a  horizontal  pipe  supported  at  equidistant  points 
the  greatest  deflection  will  be  midway  between  supports. 
The  moment  of  inertia  of  a  section  is  the  sum  of  the 
products  of  each  elementary  area  of  the  section  by  the 
square  of  its  distance  from  an  assumed  axis  of  rotation. 
It  is  a  necessary  factor  in  formulae  for  the  determination 
of  deflection  of  structures  considered  as  beams. 

The  moment  of  resistance  of  cross-section  of  a  beam  is 
the  moment  that  resists  a  bending  action  at  that  cross- 
section. 

The  section  modulus  is  the  factor  that  when  multiplied 
by  the  unit  working  strength  of  the  material  will  give  the 
moment  of  resistance  of  cross-section  of  a  structure  con- 
sidered as  a  beam. 

In  every  case  when  a  beam,  as  for  example  a  trolley 
pole  or  a  horizontal  pipe  supported  at  points,  is  subjected 
to  a  bending  action  the  following  condition  must  exist  at 
every  cross-section,  namely:  Bending  moment— motnent 


214  NATIONAL  TUBE  COMPANY. 


of  resistance  of  cross-section=unit  working  strength  of 
material  X  section  modulus. 

Example  J. — A  4  inch 
steel  pipe  has  one  end 
firmly  fixed  in  a  wall  so 
as  to  project  horizontally 
a  distance  of  8  feet.  Find 
the  greatest  safe  load  it 
will  carry  at  the  free 
end,  also  the  deflection 
with  this  load. 

Solution :  From  the  table  of  Standard  Steam  and  Gas 
Pipe,  we  see  that  the  outside  and  inside  diameters  are 
d=4.500  and  dt  =  4.026  inch.  Assuming  an  ultimate 
strength  of  material  =  60,000  Ibs.  per  sq.  inch,  and  a 
factor  of  safety  of  6,  we  get  as  a  working  unit  strength 
60,000^-6=10,000  Ibs.  From  the  table  of  Section  Moduli 
we  get 


Section  modulus =0.098  ) 

which  multiplied  by  the  unit  working  strength  gives 
Moment  of  resistance^ 


/  di4\ 

V—  r> 

rking  strengt 

/  di4 

e=980  I    d3  --- 

V  d 


d8  =(4.5)3=91.125  (see  table  of  cubes). 

dx*  (4.026)4 

log.  —  =log.  --   =4  log.  4.026—  log.  4.5=4X0.6049 
d  4.5 


—0.6532  =  1.7664,  or  —  =  58.4,  the  number  whose 
d 

log.  is  1.7664 

Then  moment  of  resistance  =980  (91.1—  58.4)=32,046  inch 
Ibs. 


NATIONAL  TUBE  COMPANY.  215 

The  bending  moment  at  support  =  WL  =  W8X12  = 
96  W  inch  Ibs.     Since  the  bending  moment  equals  the 
moment  of  resistance,  then 
96  W=32,046,  or 

W=333  Ibs.,  the  required  load. 
For  this  style  of  loading  (see  table)  the 

Wl3 
Deflection  =  -  , 


In  which  W=333,  the  safe  load  as  computed; 
I/  =96,  the  length  of  beam  in  inches; 
E=26,000,000.  the  modulus  of  elasticity; 
I  =  0.049  (d4—  dt*)  =  0.049  [  (4.54—  (4.026)4]  = 
7.21,  the  moment  of  inerta  of  cross-section. 
Substituting  these  values  in  above  formula  we  get 

333  X  (96)3 
Deflection  =  3  x  26>0OQ,000  X  7.21  =  °  53  inch' 

Example  2—  A  10 
inch     standard     lap 
welded    steel    pipe, 
carrying     water,    is 
suspended  from  the 
top  of  a  tunnel,  as 
shown  in  the  figure,  the  points  of  support  being  spaced 
at  a  distance  of  20  feet  apart. 

Find  the  deflection,  D,  due  to  the  weight  of  the  pipe 
and  its  contained  water,  on  the  supposition  that  the  pipe 
bears  equally  on  all  of  its  supports. 

Solution:  From  the  table  of  Standard  Steel  Welded  Pipe 
we  get  weight  of  pipe  per  ft.—  40.06  Ibs.,  and  weight  of 
contained  water  per  ft.  =34.  13  Ibs.,  making  a  gross  weight 
per  foot  of  74.2  Ibs.,  or  for  20  feet  a  total  weight  of  ap- 
proximately 1500  pounds. 

Since  the  pipe  is  assumed  to  run  continuously  from  one 
support  to  another,  the  deflection  will  be  greatest  midway 
between  supports,  and  will  be  the  same  as  that  for  a  beam 


B 


NATIONAL  TUBE  COMPANY. 


fixed  at  both  ends  and  uniformly  loaded.     For  this  style 
of  loading  (see  page  212)  the 

Wl3 

Deflection  — , 

384  El 
In  which  W=1500  pounds;    .  «* 

1^=20x12=240  inches; 
E= 26, 000,000,  the  modulus  of  elasticity; 
I  =  0.049  (d4— dx4)  =  0.049  [(10.75)4— (10.02)4] 
=  160,  the  moment  of  inertia  of  cross-section. 

Substituting  these  values  in  above  formula  we  get 

1500  X  (240)3 
Deflection  =  384  x  26,000,000  X  160  =0'014  inch" 

In  practice,  where  the  usual  rigid  joints  are  used,  it  is 
often  the  case  that  a  pipe  does  not  bear  equally  upon  all 
the  hangers,  and  in  cases  of  careless  erecting  or  of  shifting 
of  hangers,  the  pipe  may  not  receive  any  support  from 
one  or  more  of  the  hangers. 

Should  each  alternate  hanger,  in  the  above  example, 
become  inactive,  owing  to  any  cause,  the  maximum  de- 
flection then  would  be  that  due  to  an  unsupported  length 
of  40  feet  of  pipe.  An  inspection  of  the  formula  will  show 
that  the  deflection  of  a  beam  increases  directly  as  the 
weight  X  (length)*,  or,  for  uniformly  loaded  beams,  since 
the  weight  increases  directly  as  the  length,  as  the 
(length)*. 

Since  in  this  case  the  length  is  doubled,  the  deflection 
will  be  increased  16  fold  (that  is  24),  or  to  an  amount  = 
0.014X16=0.22  inch. 

In  the  same  manner  it  can  be  shown  that  an  unsup- 
ported portion  of  60  feet  in  length  will  deflect  or  sag 
an  amount  =  0.014  X  34  =  1.13  inch. 


NATIONAL  TUBE  COMPANY.  217 


Should  the  pipe  be 
merely  supported  at  the 
ends,  and  not  straight 
and  continuous  from 
one  support  to  another, 
then  the  conditions  would  be  those  of  a  simple  beam 
uniformly  loaded  and  supported  at  the  ends. 

By  comparing  the  deflection  formulae  for  the  case  just 
considered  and  this  case,  it  will  appear  tliat  the  deflection 
for  this  case  will  be- Jive  times  as  great;  or,  for  the  three 
cases  considered  above,  0.07,  1.10  and  5.65  inches  respec- 
tively . 

The  maximum  deflection,  or  sag,  that  should  be  permit- 
ted in  practice  will  depend  ordinarily  upon  the  effective 
thickness  of  wall  of  pipe  and  the  unit  working  strength 
of  the  material  composing  it . 

The  effective  thickness  of  pipe  in  any  particular  case  will 
be  the  thickness  remaining  after  deducting  the  depth  of 
screw-thread  (for  wrought  pipe  with  threaded  ends 
for  coupling  or  flange  connections)  plus  a  reasonable 
amount  for  the  deterioration  due  to  corrosion,  or  other 
causes;  which  amount  will  depend  upon  the  nature  of  the 
service  and  the  expected  life  of  pipe. 

In  every  practical  example  the  effective  thickness  of 
pipe  should  be  used  in  applying  all  formulae  relating  to 
strength  of  pipe  to  resist  either  bending  or  bursting. 


STRESS   DUE   TO   INTERNAL   BURSTING 
PRESSURE, 

Owing  to  the  difference  in  the  nature  of  the  stress 
occuring  in  thin  and  thick  walls  of  cylinders,  pipes,  etc., 
when  subjected  to  a  fluid  pressure,  it  will  be  necessary 
to  divide  them  into  two  classes,  namely,  those  having 
thin  walls  and  those  having  thick  walls.  In  the  follow- 
ing discussion  only  those  having  thin  walls  will  be  con- 
sidered. 


NATIONAL  TUBE  COMPANY. 


Let  d  =  internal  diameter  in  inches  ; 

t  =  thickness  of  cylinder  wall  in  inches  ; 
p  =  internal  fluid  pressure,  Ibs.  per  sq.  inch  ; 
TT=  3.1416; 

ft=  unit  working  strength  in  tension  ; 
fc=    "  "          "  compression ; 

fs—    "          "  "          "  shear ; 

strength  of  joint, 
e  =  efficiency  of  joint,  or  strength  of  plate' 

c  =  thickness  of  metal,  in  inches,  allowed  for  wast- 
ing away  due  to  corrosion,  or  other  causes. 


STRENGTH  OF  THIN  CYLINDERS  TO  RESIST 
BURSTING, 

The  force  tending  to 
tear  the  plate  along  a 
line  lying  circumfer- 
entially  around  the 
cylinder,  as,  for  ex- 
ample, along  the  sec- 
tion lying  in  the  plane  A  B,  will  equal  the  fluid  pressure 
exerted  on  one  end  of  the  cylinder,  which  equals  the 
area  of  a  cross-section  of  cylinder  in  square  inches  X  in- 
ternal pressure  per  square  inch,  or 

Longitudinal  bursting  pressure  )       *&* 

tending  to  rupture  circumferentially   f  —    ^   P- 

This  bursting  pressure  will  be  resisted  by  the  tenacity 
of  the  metal  whose  cross-section  lies  in  the  plane  A  B, 
which  equals  the  circumference,  or  distance  around  the 
cylinder,  multiplied  by  the  thickness  of  the  metal.  Hence 

Resistance  to  bursting  pressure  )  =  T  d  t  f 

tending  to  rupture  circumferentially   f 

Since  the  resistance  to  the  bursting  pressure  must  equal 
the  pressure  itself,  we  have 

Trd2  dp  4  f  1 1 

Trd  t  ft.  = p,  or  t  = ;  p  = . 

4  4ft  d 


NATIONAL  TUBE  COMPANY.  219 


The  force  tending  to 
tear  the  plate  along  a 
—k  1-4  line  extending  longi- 
tudinally,  as,  for  ex- 
ample, along  the  sec- 
tion lying  in  the  plane  C  D,  will  equal  the  sum  of  the 
normal  components  of  the  fluid  pressures  on  the  inner 
surface  of  the  cylinder,  which  it  can  be  shown  is  the 
same  as  the  fluid  pressure  on  a  surface  equal  to  the 
length  of  the  cylinder  multiplied  by  its  diameter,  or  d  1. 
We  then  have 

Transverse  bursting  pressure          I  =  d  1  o 
Tending  to  rupture  longitudinally  J 

This  bursting  pressure  will  be  resisted  by  the  tenacity 
of  the  metal  whose  cross-section  lies  in  the  plane  C  D, 
which  latter  equals  twice  the  length  of  cylinder  multi- 
plied by  the  thickness  of  the  metal.  Hence 

Resistance  to  bursting  pressure       )   =  3  1  t  f 
Tending  to  rupture  longitudinally  ) 

Since  the  resistance  to  the  bursting  pressure  must  equal 
the  pressure  itself,  we  have 

dp  2  f 1 1 

2  1 1  ft  =  d  1  p,  or  t  =  — ;  p  =  . 

2ft  d 

From  a  comparison  of  the  above  formulae,  it  will  be  seen 
that  the  force  due  to  a  fluid  pressure  within  a  pipe,  boiler, 
or  other  cylindrical  vessel,  that  tends  to  cause  rupture 
longitudinally  is  twice  that  which  tends  to  cause  rupture 
transversely,  that  is  circumferentially  or  around  the 
pipe. 

.  From  the  above  relations,  then,  it  will  appear  that  a 
pipe,  or  other  cylindrical  vessel  having  walls  of  uniform 
thickness,  when  subjected  to  a  fluid  pressure  only,  will 
always  tend  to  rupture  longitudinally.  The  strength  at 
the  joints,  resisting  rupture  transversely,  may  be  reduced 
by  the  cutting  of  threads  or  riveting  to  flanges,  or  other- 
wise, to  an  amount  equal  to  one-half  the  strength  of  the 


NATIONAL  TUBE  COMPANY. 


metal  of  pipe  in  cross-section,  without  altering  the  ten- 
dency of  the  pipe  to  rupture  longitudinally. 

Example  J»  —  Find  the  safe  working  pressure  and  also 
the  bursting  pressure  of  a  standard  10-inch  lap-welded 
steel  pipe,  having  plain  ends,  or  welded  heads. 

Solution:  Assuming  that  the  pipe  is  not  subjected  to 
shock  or  vibration,  we  will  assume  a  unit  working  strength 
of  material  =10,  000  Ibs.,  which  allows  a  factor  of  safety 
of  6  on  the  assumption  that  the  ultimate  tensile  strength 
is  60,000  Ibs.  per  sq.  inch. 

Then  in  the  formula  for  the  internal  fluid  pressure. 
Sfftt 


ft  =10,000  Ibs.,  the  unit'  working  strength  of  material; 
t  =  0.366  inch,  the  thickness  of  wall  of  pipe; 
d  =10.385,  the  diameter  of  pipe. 
Substituting  these  values  we  get 

2  X  10.000  X  0.366 
P=  --  10385  =  70o  Ibs.  per  sq.  in. 

The  bursting  pressure,  on  the  above  assumption,  would 
be  six  times  the  working  pressure,  or 

Bursting  pressure  =705X6  =4,  230  Ibs.  per  sq.  in. 

Example  2.  —  Find  the  working  ^pressure  for  the  pipe 
given  in  example  1,  when  provision  is  made  for  wasting 
away  of  the  metal  by  corrosion,  or  otherwise,  so  as  to 
reduce  the  thickness  of  the  walls  by  y&  inch. 

Then  t=0.366—  0.125=0.241  inch,  the  thickness  of  wall 
after  corrosion  of  y&  inch  has  occurred,  the  other  values 
remaining  the  same  as  before.  Substituting  in  the  form- 
ula for  pressure  we  get 

2  X  10,000  X  0,241 
p  =  —  -  =  465  Ibs.  per  sq.  in. 

10.385 

In  practice  it  is  often  necessary  to  provide,  especially 
in  steam  and  water  pipes,  for  stresses  due  to  vibration, 
shock,  temperature  changes  and  various  other  causes,  in 
which  case  the  factor  of  safety  of  six  assumed  in  the 
above  examples  should  be  increased  to  from  8  to  15  for 


NATIONAL  TUBE  COMPANY. 


wrought  pipe,  depending  upon  the  severity  of  these 
actions  . 

Assuming  a  factor  of  safety  of  12,  the  safe  working 
pressure  in  the  above  examples  would  be  for  Example  1, 
350  Ibs.  per  sq.  in.,  and  for  example  2,  230  Ibs.  per  sq. 
inch. 

Example  3*  —  Find  the  thickness  of  a  mild  steel  seamless 
cylindrical  receiver,  20  inches  in  diameter,  to  contain 
air  at  2,000  Ibs.  per  sq.  in.  gauge  pressure  . 

Solution:  Assuming  a  unit  working  strength  of  material 
of  12,000  Ibs.  then  in  the  formula  for  thickness, 


2ft 

d—  20,  the  diameter  of  receiver  in  inches; 
p—  2,000,  the  internal  pressure  in  Ibs.  per  sq.  inch; 
ft—  12,000,  the  working  strength  persq.  in.  of  material; 
Substituting  these  values  in  the  formula  we  get 
20  X  2,000 


In  tubular  construction,  having  longitudinal  riveted 
joints  intended  to  resist  internal  fluid  pressure,  the  form- 
ulae for  thickness  of  wall  and  for  safe  working  pressure 
will  become 

dp  2e  f  1  1 

t=  -  ;  p  =  -  ; 

2e  ft  d 

In  which  d=  diameter  of  vessel  in  inches; 
t=  thickness  of  wall  in  inches; 
p=internal  fluid  pressure,  Ibs.  per  sq.  inch; 
ft=:  unit  working  strength  of  material  in  tension; 
e=efficiency  of  riveted  joint,  from  0.6  to  0.8. 
To  provide  in  practice  for  wasting  away  of  the  metal, 
due  to  corrosion,  or  other  causes,  the  above  formulae  will 
become 

dp  2  eft  (t—  c) 

t=  -  -fc;  p=  --  . 

3eft  d 


Or 

222  NATIONAL  TUBE  COMPANY. 

Where  c=reduction  in  the  thickness,  in  inches,  of  the 
metal  constituting  the  wall  of  the  vessel,  because  of  the 
wasting  away  of  the  metal  in  practice  due  to  corrosion 
and  other  causes . 

Example  4» — Find  the  thickness  of  plate  for  a  60-inch 
steam  boiler,  to  carry  100  Ibs.  gauge  pressure,  the  longi- 
tudinal riveted  joints  having  an  efficiency  of  0.7,  the 
ultimate  tensile  strength  of  the  material  being  60,000  Ibs. 
per  sq.  inch. 

Solution:  Assuming  an  actual  factor  of  safety  of  five 
and  allowing  ^  inch  for  wasting  away  of  plates  during 
the  life  of  the  boiler,  we  have  in  the  above  formula  for 
thickness  of  plate: 

d=60,  the  diameter  of  boiler  in  inches; 
p=100,  the  gauge  pressure  per  sq.  inch; 
ft=12,000,  the  unit  working  strength  of  material; 
e=0.7,  the  efficiency  of  longitudinal  joint; 
c=0.125,  the  allowance  for  corrosion,  etc. 
Substituting  these  values  in  the  formula  we  get 

60  X  100 
t=SX  0.7  X  12,000  +0.185=0.48^1.. 

Example  5. — Find  the  greatest  steam  pressure  that 
could  be  carried  by  the  boiler,  in  Example  4,  when  new, 
that  is,  before  any  wasting  away  of  metal  has  occurred, 
all  other  conditions  being  the  same. 

Solution:  Making  c  =  0  in  the  above  equation,  we  get 
dp  2  e  f  1 1 

t  = ;  and  p  = ; 

2eft  d 

Which  are  the  general  equations  for  the  thickness,  t,  in 
inches  and  safe  fluid  pressure,  p,  in  Ibs,  per  sq.  inch,  for 
pipes  or  other  cylindrical  vessels  having  longitudinal 
riveted  joints. 

Substituting  the  values,  given  in  Example  4,  in  the 
above  formula  for  pressure,  we  get 

2  X  0.7  X  12,000  X  0.48 
p  =•  — — —  =  135  Ibs.  gauge. 


NATIONAL  TUBE  COMPANY. 


In  Examples  4  and  5  an  actual  factor  of  safety  at  the 
longitudinal  joints  is  assumed,  which  makes  the  apparent 
factor  of  safety,  that  is,  the  factor  of  safety  on  the  plate 
itself,  for  the  assumed  conditions,  =5-7-0.7=7.1. 

In  practice  an  apparent  factor  of  safety  of  5  is  often 
used,  for  double  riveted  longitudinal  lap  joints,  resulting 
in  an  actual  factor  of  safety  of  5  X  (0.68  to  0.72)=  from  3.4 
to  3.6.  Very  often  no  allowance  is  made  for  the  wasting 
away  of  the  metal,  which  fact  in  conjunction  with  the 
use  of  too  small  a  factor  of  safety  will  account  for  a  large 
number  of  the  boiler  explosions  that  have  occurred  in 
practice. 


STRENGTH  OF  CYLINDER  ENDS  OR  HEADS. 

/  The  ends  or  heads  of  a 

cylindrical  vessel  intended 
to  contain  a  fluid  under 
pressure,  should  be  de- 
signed  so  as  to  be  as  strong 
as  the  cylindrical  part  of 
the  vessel.  This  can  ordin- 
arily be  best  accomplished 

by  giving  the  end  the  form  of  a  portion  of  a  hollow 
sphere,  as  shown  in  the  figure,  whose  radius  equals  the 
diameter  of  the  cylindrical  part,  in  which  case  to  be 
equally  strong  throughout  the  thickness  should  be  the 
same  as  that  of  the  cylindrical  part.  This  is  because  of 
the  fact  that  for  a  given  internal  fluid  pressure,  the  stress 
created  in  the  walls  of  a  thin  hollow  cylinder  will  be  the 
same  as  that  created,  for  the  same  pressure,  in  the  walls 
of  a  thin  hollow  sphere  of  double  the  diameter. 

The  use  of  flat  ends  should  be  avoided,  except  for  con- 
structions such  as  tube  plates,  where  they  are  desirable 
because  of  constructional  reasons  and  can  be  easily 
stayed . 


224                       NATIONAL  TUBE  COMPANY 

f  HOLLOW,  CYLINDRICAL,  WROUGHT  IRON  PILLARS.—  BREAKING  LOADS  IN  TONS. 

CALCULATED  BY  GORDON'S  FORMULA  (TRAUTWINE.)  THICKNESS  ^  INCH. 

OUTER  DIAMETERS  IN  INCHES. 

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230                      NATIONAL  TUBE  COMPANY.    • 

WEIGHT  OF  RIVETS  IN  POUNDS  PER  JOO. 

Length  from  under  head.     One  cubic  ft.  weighing  480  Ibs. 

Length 

M" 

K" 

H' 

%" 

y& 

1" 

It/" 

iw 

Inches. 

Diam. 

Diam. 

Diam. 

Diam. 

Diam. 

Diam. 

Diam. 

Diam. 

IK 

5.4 

12.6 

21.5 

28.7 

43.1 

65.3 

91.5 

123. 

1  ix 

6.2 

13.9 

23.7 

31.8 

47.3 

70.7 

98.4 

133. 

1% 

6.9 

15.3 

25.8 

34.9 

51.4 

76.2 

105. 

142. 

2 

7.7 

16.6 

27.9 

37.9 

55.6 

81.6 

112. 

150. 

2^ 

8.5 

18.0 

30.0 

41.0 

59.8 

87.1 

119. 

159. 

2V 

9.2 

19.4 

32.2 

44.1 

63.0 

92.5 

126. 

167. 

sg 

10.0 

20.7 

34.3 

47.1 

68.1 

98.0 

133. 

176. 

3 

10.8 

22.1 

36.4 

50.2 

72.3 

103. 

140. 

184. 

3K 

11.5 

23.5 

38.6 

53.3 

76.5 

109. 

147. 

193. 

31^ 

12.3 

24.8 

40.7 

56.4 

80.7 

114. 

154. 

201. 

^M 

13.1 

26.2 

42.8 

59.4 

84.8 

120. 

161. 

210. 

4 

13.8 

27.5 

45.0 

62.5 

89.0 

125. 

167. 

218. 

4K 

14.6 

28.9 

47.1 

65.6 

93.2 

131. 

174. 

227. 

4/1> 

15.4 

30.3 

49.2 

68.6 

97.4 

136. 

181. 

236. 

^M 

16.2 

31.6 

51.4 

71.7 

102. 

142. 

188. 

244. 

5 

16.9 

33.0 

53.5 

74.8 

106. 

147. 

195. 

253. 

5K 

17.7 

34.4 

55.6 

77.8 

110. 

153. 

202. 

261. 

5i/ 

18.4 

35.7 

57.7 

80.9 

114. 

158. 

209. 

270. 

5// 

19.2 

37.1 

59.9 

84.0 

118. 

163. 

216. 

278. 

6 

20.0 

38.5 

62.0 

87.0 

122. 

169. 

223. 

287. 

6i^ 

21.5 

41.2 

66.3 

93.2 

131. 

180. 

236. 

304. 

7  2 

23.0 

43.9 

70.5 

99.3 

139. 

191. 

250. 

321. 

71^ 

24.6 

46.6 

74.8 

106. 

147. 

203. 

264. 

338. 

8 

26.1 

49.4 

79.0 

112. 

156. 

213. 

278. 

355. 

gjy 

27.6 

52.1 

83.3 

118. 

164. 

223. 

292. 

372. 

9  2 

29.2 

54.8 

87.6 

124. 

173. 

234. 

306. 

389. 

9i/ 

30.7 

57.6 

91.8 

130. 

181. 

245. 

319. 

406. 

10 

32.2 

60.3 

96.1 

136. 

189. 

256. 

333. 

423. 

10^ 

33.8 

63.0 

101. 

142. 

198. 

267. 

347. 

440. 

11  2 

35.3 

65.7 

105. 

148. 

206. 

278. 

361. 

457. 

11/4 

36.8 

68.5 

109. 

155. 

214. 

289. 

375. 

474. 

12 

38.4 

71.2 

113. 

161. 

223. 

300. 

388. 

491. 

Heads 

1.8 

5.7 

10.9 

13.4 

22.2 

38.0 

57.0 

82.0 

•^QC^                                                               —  j_»^ 

NATIONAL  TUBE  COMPANY. 


WEIGHT   IN   POUNDS   OF    JOO    BOLTS   WITH 

SQUARE   HEADS    AND   NUTS, 

One  cubic  foot  weighing  480  Ibs. 


t 
J 

DIAMETER  OF  BOLT,  INCHES. 

M 

A 

% 

A 

u 

% 

« 

% 

1 

2  4 
3  4 

5* 

4^ 
5 

h 

6H 

3* 

9 

10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 

4.0 
4.4 
4.7 
5.1 
5.4 
5.8 
6.1 
6.8 
7.5 
8.2 
8.9 
9.6 
10.3 
11.0 
11.7 
12.4 
13.1 

6.8 
7.3 
7.8 
8.4 
8.9 
9.5 
10.0 
11.1 
12.2 
13.2 
14.3 
15.4 
16.5 
17.6 
18.6 
19.7 
20.8 

10.6 
11.3 
12.0 
12.6 
13.3 
14.0 
14.7 
16.0 
17.4 
18.7 
20.0 
21.4 
22.8 
24.1 
25.9 
27.7 
29.5 
33.1 
36.7 
40.4 
44.0 

15.0 
16.1 
17.2 
18.2 
19.2 
20.2 
21.2 
23.2 
25.2 
27.2 
29.1 
31.2 
33.1 
35.1 
37.1 
39.1 
41.0 
45.0 
49.0 
53.0 
57.0 

23.9 
25.1 
26.3 
27.7 
29.0 
30.4 
31.8 
34.7 
37.5 
40.2 
43.0 
45.7 
48.4 
51.2 
54.0 
56.7 
59.4 
64.8 
70.3 
75.8 
81.3 
86.7 
92.2 
97.7 
103.1 
108.6 
114.1 
119.5 
125.0 

40.5 
42.7 
44.8 
47.0 
49.2 
51.4 
53.5 
57.9 
62.3 
66.7 
71.0 
75.4 
79.8 
84.1 
88.5 
92.9 
97.2 
106.0 
114.7 
123.5 
132.2 
140.7 
149.2 
157.6 
166.1 
174.6 
183.1 
191.5 
200.0 

70.0 
73.1 
76.2 
79.3 
82.4 
85.5 
88.7 
95.0 
101.2 
107.5 
113.7 
120.0 
126.2 
132.5 
138.7 
145.0 
151.2 
163.7 
176.2 
188.7 
201.0 
213.4 
225.9 
238.3 
250.8 
263.2 
275.6 
288.1 
300.5 

m.s 

124.7 
128.9 
137.4 
145.8 
159.2 
167.7 
176.1 
184.6 
193.0 
201.4 
209.9 
218.3 
240.2 
257.1 
273.9 
290.0 
307.7 
324.5 
341.4 
358.3 
375.2 
392.0 
408.9 
425.8 

iss'.o 

196.0 
207.0 
218.0 
229.0 
240.0 
251.0 
262.0 
273.0 
284.0 
295.0 
317.0 
339.0 
360.0 
382.0 
404.0 
426.0 
448.0 
470.0 
492.0 
514.0 
536.0 
558.0 

Per  in. 
addi- 
tional. 

1.4 

2.2 

3.6 

4.0 

5.5 

8.5 

12.4 

16.9 

22.0 

APPROXIMATE  WEIGHT   OF  NUTS  AND  BOLT 
HEADS  IN  POUNDS. 


Diam.  of  Bolt  in  Inches 

X 

T6B 

% 

T7* 

-Jt 

% 

« 

Weight  of  Hexagon  ) 
Nut  and  Head  j 

.017 

.042 

.057 

.109 

.128 

.267 

.43 

Weight  of  Square! 
Nut  and  Head  f 

.021 

.049 

.069 

.120 

.164 

.320 

.55 

Diam.  of  Bolt  in  Inches 

% 

1 

1J4 

1« 

1% 

2 

2^ 

Weight  of  Hexagon  j 
Nut  and  Head.   ...f 

.73 

1.10 

2.14 

3.78 

5.6 

8.75 

17.0 

Weight  of  Square) 
Nut  and  Head  ....f 

.88 

1.81 

2.56 

4.42 

7.0 

10.5 

21.0 

} 

232                      NATIONAL  TUBE  COMPANY. 

Sizes  and  Weights  of  Hot  Pressed  Hexagon  Nuts, 

The  sizes  are  the  usual  manufacturers',  not  the  Franklin  Institute  Standard.    Both 

weights  and  sizes  are  for  unfin  shed  Nuts.    One  cubic  foot  weighing  480  Ibs. 

Size  of 
Bolt. 

Weight 
of  100 
Nuts. 

Rough 
Hole. 

Thickness 
Of  Nut. 

Short 
Dia- 
meter. 

Long 
Dia- 
meter. 

No.  of 
Nuts  in 
100  Ibs. 

% 

1.3 

ft 

/£ 

M 

.58 

8000. 

5 

2.4 

ii 

6 

5/ 

.72 

4170. 

¥ 

4.1 

% 

M 

.87 

2410. 

6.8 

It 

A 

% 

1.01 

1460. 

% 

7.1 

7 

K 

% 

1.01 

1410. 

/4 

9.8 

TIT 

/4 

l 

1.15 

1020. 

ft 

14.0 

% 

ft 

1^ 

1.30 

710. 

5// 

14.7 

ft 

% 

!^ 

1.30 

680. 

5/ 

19.1 

T»T 

% 

1M 

1.44 

520. 

% 

22.9 

ft 

% 

IK 

1.44 

440. 

% 

27.2 

11 

% 

1M 

1.59 

370. 

% 

39. 

1? 

^/ 

\5/ 

1.73 

256. 

% 

44. 

25 

7/ 

ll/ 

1.88 

226. 

50. 

ft 

1 

!^ 

1.88 

198. 

\ 

57. 

% 

1 

!^ 

2.02 

176. 

1 

64. 

& 

^l/ 

13/ 

2.02 

156. 

96. 

H 

1M 

2 

2.31 

104. 

i& 

134. 

IT* 

1M 

2J/X 

2.60 

75. 

1% 

180. 

1ft 

11^ 

2% 

2.89 

56. 

1H 

235. 

!^ 

2% 

3.18 

42. 

1 

300. 
370. 
460. 

i 

I1 

3 

3.46 
3.75 
4.04 

33.4 

26.7 
21.5 

2 

450. 
560. 

IS 

2 

33j 

4.04 
4.33 

22.4 

18.0 

2>| 

560. 

2 

2^ 

4.33 

17.7 

2% 

680. 

2i/ 

2M 

4 

4.62 

14.7 

810. 

2}J 

41^ 

4.91 

12.3 

2?J 

980. 

2Tff 

2^ 

4k 

5.20 

10.2 

3 

1150. 

2H 

3 

4% 

5.48 

8.7 

1340. 

21  5 

3/^ 

5 

5.77 

7.5 

3/^ 

1580. 

3S 

3J^ 

514 

6.06 

6.3 

NATIONAL  TUBE  COMPANY.                      233 

Sizes  and  Weights  of  Hot  Pressed  Square  Nuts. 

weights  and  sizes  are  for  unfinished  Nuts.     One  cubic  foot  weighing  480  Ibs. 

Size  of 
Bolt. 

Weight 
of  100 

Nuts. 

Rough 
Roll 

Thickness 
Of  Nut. 

Side  of 
Square 

Diagonal 

No.  of 
Nuts  in 
100  Ibs 

¥ 

1.5 

A 

K 

1^ 

.71 

6800. 

2.9 

ft 

/'8 

.88 

3480. 

% 

4.9 

H 

E 

/I 

1.06 

2050. 

Tff 

7.7 

H 

A 

^ 

1.24 

1290. 

^ 

8.6 

/^ 

K 

1.24 

1170. 

H 

11.8 

s 

s 

1 

1.41 

850. 

9 

16.7 

1£ 

TV 

11^ 

1.59 

600. 

% 

17.7 

A 

5/ 

\y^ 

1.59 

570. 

% 

22.8 

1^ 

IK 

1.77 

440. 

¥ 

32.3 

H 

M 

1% 

1.94 

310. 

39.8 

H 

/€ 

11^ 

2.12 

251. 

% 

53. 

ft 

Jg 

1^ 

2.30 

190. 

7/s 

63. 

^8 

!M 

2.47 

159. 

1 

68. 

% 

1 

!M 

2.47 

146. 

.  1 

94. 

-% 

1 

2 

2.83 

106. 

IL/ 

103. 

16 

jr/ 

2 

2.83 

97. 

1H 

137. 

if 

1^ 

2M 

3.18 

73. 

*K 

145. 

IT* 

IK 

2K 

3.18 

69. 

IK 

186. 

IT* 

IK 

2/^ 

3.54 

54. 

1% 

247. 

!A 

1% 

2M 

3.89 

41. 

IK 

319. 

1  6 

!M 

3 

4.24 

31.3 

15£ 

400. 

IA 

\S£ 

3K 

4.60 

24.8 

19^ 
*/8 

500. 
620. 

1 

1% 

1/Q 

sM 

4.95 
5.30 

19.9 
16.2 

2 

750. 

IT! 

2 

4 

5.66 

13.4 

2/^ 

780. 

\y^ 

2/^ 

4 

5.66 

12.8 

2K 

930. 

2 

2K 

4K 

6.01 

10.7 

2% 

960. 

2^ 

2% 

4M 

6.01 

10.4 

1130. 

2K 

4^/ 

6.36 

8.9 

2^ 

1370. 

2Tff 

2M 

4^ 

6.72 

7.3 

3 

1610. 

2  1.1 

3 

5 

7.07 

6.2 

3K 

2110. 

2{| 

3K 

7.78 

4.7 

3>| 

2750. 

3i/| 

3K 

6  2 

8.49 

3.6 

rr  

'      234                     NATIONAL  TUBE  COMPANY. 

STANDARD  GAUGES. 

I 

THICKNESS  IN  DECIMALS  OF  AN  INCH. 

rt 

o 

o 

ingham 
or 

Browne  & 

United 

British 

Wash- 
burn  & 

Trenton 

Stubs 

0* 

Stubb's 
Iron 

Sharpe 

States 

Imperial 

Moen 
Co. 

Iron  Co. 

Steel 
Wire 

* 

Wire 

~^0 

.50000 

.500 

6° 

46875 

464 

5° 

.43750 

!432 

.45 

4° 

.'454 

.46000 

.40625 

.400 

.'3938 

.40 

3° 

.425 

!40964 

.37500 

.372 

.3625 

.36 

2° 

.380 

.36480 

.34375 

.348 

.3310 

.33 

0 

.340 

.32486 

.31250 

.324 

.3065 

.305 

1 

.300 

.28930 

.28125 

.300 

.2830 

.285 

!227 

2 

.284 

.25763 

.26562 

.276 

.2625 

.265 

.219 

3 

.259 

.22942 

.25000 

.252 

.2437 

.245 

.212 

4 

.238 

.20431 

.23437 

.232 

.2253 

.225 

.207 

5 

.220 

.18194 

.21875 

.212 

.2070 

.205 

.204 

6 

.203 

.16202 

.20312 

.192 

.1920 

.190 

.201 

7 

.180 

.14428 

.18750 

.176 

.1770 

.175 

.199 

8 

.165 

.12849 

.17187 

.160 

.1620 

.160 

.197 

9 

.148 

.11443 

.15625 

.144 

.1483 

.145 

.194 

10 

.134 

.10189 

.14062 

.128 

.1350 

.130 

.191 

11 

.120 

.09074 

.12500 

.116 

.1205 

.1175 

.188 

12 

.105 

.08081 

.10937 

.104 

.1055 

.1050 

.185 

13 

.095 

.07196 

.09375 

.092 

.0915 

.0925 

.182 

14 

.083 

.06408 

.07812 

.080 

.0800 

.0800 

.180 

15 

.072 

.05707 

.07031 

.072 

.0720 

.0700 

.178 

16 

.065 

.05082 

.06250 

.064 

.0625 

.0610 

.175 

17 

.058 

.04526 

.05625 

.056 

.0540 

.0525 

.172 

18 

.049 

.04030 

.05000 

.048 

.0475 

.0450 

.168 

19 

.042 

.03589 

.04375 

.040 

.0410 

.0400 

.164 

20 

.035 

.03196 

.03750 

.036 

.0348 

.0350 

.161 

21 

.032 

.02846 

.03437 

.032 

.0317 

.0310 

.157 

22 

.028 

.02535 

.03125 

.028 

.0286 

.0280 

.155 

23 

.025 

.02257 

.02812 

.024 

.0258 

.0250 

.153 

24 

.022 

.02010 

.02500 

.022 

.0230 

.0225 

.151 

25 

.020 

.01790 

.02187 

.020 

.0204 

.0200 

.148 

26 

.018 

.01594 

.01875 

.018 

.0181 

.0180 

.146 

27 

.016 

.01419 

.01719 

.0164 

.0173 

.0170 

.143 

28 

.014 

.01264 

.01562 

.0148 

.0162 

.0160 

.139 

29 

.013 

.01126 

.01406 

.0136 

.0150 

.0150 

.134 

30 

.012 

.01002 

.01250 

.0124 

.0140 

.0140 

.127 

31 

.010 

.00893 

.01094 

.0116 

.0132 

.0130 

.120 

32 

.009 

.00795 

.01016 

.0108 

.0128 

.0120 

.115 

33 

.008 

.00708 

.00938 

.0100 

.0118 

.0110 

.112 

34 

.007 

.00630 

.00859 

.0092 

.0104 

.0100 

.110 

35 

.005 

00561 

.00781 

.0084 

.0095 

.0095 

.108 

36 

.004 

.00500 

.00703 

.0076 

.0090 

.0090 

.106 

37 

.00445 

.00664 

.0068 

.0085 

.103 

38 

.00396 

.00625 

.0060 

.0080 

.101 

39 

.00353 

.0075 

.099 

40 

" 

.00314 

.0070 

.097 

NATIONAL  TUBE  COMPANY.         235 

DECIMALS  OF  AN  INCH  AND  FOOT  FOR 

EACH  *V 

a 

o 

Decimals 

Decimals 

§ 

Decimals 

Decimals 

5 

*W 

r   of  an 
Inch. 

of  a 
Foot. 

1 

aV 

& 

of  an 
Inch. 

of  a 
Foot. 

£ 

fa 

[  .015625 

.0013 

33 

.515625 

.0430 

i 

.031250 

.0026 

17 

.531250 

.0443 

, 

3  .046875 

.0039 

35 

.546875 

.0456 

Tv 

.062500 

.0052 

T9* 

.562500 

.0469 

5  .078125 

.0065 

37 

.578125 

.0472 

3 

.093750 

.0078 

19 

.593750 

.0495 

7  .109375 

.0091 

39 

.609375 

.0508 

y& 

.125000 

.0104 

% 

.625000 

.0521 

3  .140625 

.0117 

41 

.640625 

.0534 

5 

.156250 

.0130 

21 

.656250 

.0547 

1 

1  .171875 

.0143 

43 

.671875 

.0560 

T3ff 

.187500 

.0156 

H 

.687500 

.0573 

1 

3  .203125 

.0169 

45 

.703125 

.0586 

7 

.218750 

.0182 

23 

.718750 

.0599 

1 

5  .234375 

.0195 

47 

.734375 

.0612 

M 

.250000 

.0208 

% 

.750000 

.0625 

1 

7  .265625 

.0221 

49 

.765625 

.0638 

9 

.281250 

.0234 

25 

.781250 

.0651 

1 

9  .296875 

.0247 

51 

.796875 

.0664 

A 

.312500 

.0260 

ft 

.812500 

.0677 

2 

1  .328125 

.0273 

53 

.828125 

.0690 

11 

.343750 

.0286 

27 

.843750 

.0703 

2 

3  .359375 

.0299 

55 

.859375 

.0716 

M 

.375000 

.0313 

% 

.875000 

.0729 

2 

5  .390625 

.0326 

57 

.890625 

.0742 

13 

.406250 

.0339 

29 

.906250 

.0755 

2 

7  .421875 

.0352 

59 

.921875 

.0768 

.437500 

.0365 

if 

.937500 

.0781 

Tff 

2 

9  .453125 

.0378 

61 

.953125 

.0794 

15 

.468750 

.0391 

31 

.968750 

.0807 

3 

1  .484375 

.0404 

63 

.984375 

.0820 

8 

.500000 

.0417 

1 

1.000000 

.0833 

DECIMALS  OF  A  FOOT  FOR  EACH  INCH. 

In    Ft. 

[n.   Ft.    I 

i.    Ft. 

n.   Ft. 

n.    Ft. 

In.    Ft. 

1  .0833 

3  .2500 

5  .4167 

7  .5833 

9  .7500 

11  .9167 

2  .1667 

4  .3333 

6  .5000 

8  .6667 

LO  .8333 

121.0000 

ID  ,  

236                     NATIONAL  TUBE  COMPANY. 

WEIGHTS  OF  SHEETS  AND  PLATES  OF  STEEL, 

WROUGHT  IRON,  COPPER  AND  BRASS. 

BIRMINGHAM  GAUGE. 

No.  of 

Thickness 

WEIGHT  PER  SQUARE  FOOT. 

Gauge. 

in  Inches. 

Steel. 

Iron. 

Copper. 

Brass. 

0000 

.454 

18.5232 

18.16 

20.5662 

19.4312 

000 

.425 

17.3400 

17.00 

19.2525 

18.1900 

00 

.380 

15.5040 

15.20 

17.2140 

16.2640 

0 

.340 

13.8720 

13.60 

15.4020 

14.5520 

1 

.300 

12.2400 

12.00 

13.5900 

12.8400 

2 

.284 

11.5872 

11.36 

12.8652 

12.1552 

3 

.259 

10.5672 

10.36 

11.7327 

11.0852 

4 

.238 

9.7104 

9.52 

10.7814 

10.1864 

5 

.220 

8.9760 

8.80 

9.966 

9.4160 

6 

.203 

8.2824 

8.12 

9.1959 

8.6884 

7 

.180 

7.3440 

7.20 

8.1540 

7.7040 

8 

.165 

6.7320 

6.60 

7.4745 

7.0620 

9 

.148 

6.0384 

5.92 

6.7044 

6.3344 

10 

.134 

5.4672 

5.36 

6.0702 

5.7352 

11 

.120 

4.8960 

4.80 

5.4360 

5.1360 

12 

.109 

4.4472 

4.36 

4.9377 

4.6652 

13 

.095 

3.8760 

3.80 

4.3035 

4.0660 

14 

.083 

3.3864 

3.32 

3.7599 

3.5524 

15 

.072 

2.9376 

2.88 

3.2616 

3.0816 

16 

.065 

2.6520 

2.60 

2.9445 

2.7820 

17 

.058 

8.3664 

2.32 

2.6274 

2.4824 

18 

.049 

1.9992 

1.96 

2.2197 

2.0972 

19 

.042 

1.7136 

1.68 

1.9026 

1.7976 

20 

.035 

1.4280 

1.40 

1.5855 

1.4980 

21 

.032 

1.3056 

1.28 

1.4496 

1.3696 

22 

.028 

1.1424 

1.12 

1.2684 

1.1984 

23 

.025 

1.0200 

1.00 

1.1325 

1.0700 

24 

.022 

.8976 

.88 

.9966 

.9416 

25 

.020 

.8160 

.80 

.9060 

.8560 

26 

.018 

.7344 

.72 

.8154 

.7704 

27 

.016 

.6528 

.64 

.7248 

.6848 

28 

.014 

.5712 

.56 

.6342 

.5992 

29 

.013 

.5304 

.52 

.5889 

.5564 

30 

.012 

.4896 

.48 

.5436 

.5136 

31 

.010 

.4080 

.40 

.4530 

.4280 

32 

.009 

.3672 

.36 

.4077 

.3852 

33 

.008 

.3264 

.32 

.3624 

.3424 

34 

.007 

.2856 

.28 

.3171 

.2996 

35 

.005 

.2040 

.20 

.2265 

.2140 

36 

.004 

.1632 

.16 

.1812 

.1712 

Specific  Gravities  
Weight  of  a  Cubic  Ft. 
1     In. 

7.85 
489.6 
0.2833 

7.70 
480.0 

0.2778 

8.72 
543.6 
0.3146 

8.24 
513.6 
0.2972 

SL  :  $ 

gf^—  ** 

NATIONAL  TUBE  COMPANY,                      237 

WEIGHTS  OF  SHEETS  AND  PLATES  OF  STEEL, 

WROUGHT  IRON,  COPPER  AND  BRASS. 

AMERICAN  OR  BROWNE  &  SHARPE  GAUGE. 

No.  of 
Gauge. 

Thickness 
n  Inches. 

WEIGHT  PER  SQUARE  FOOT. 

Steel. 

Iron. 

Copper. 

Brass. 

0000 
000 
00 

.460000 
.409642 
.364796 

18.7680 
16.7134 
14.8837 

18.4000 
16.3857 
14.5918 

20.8380 
18.5568 
16.5253 

19.6880 
17.5327 
15.6133 

0 
1 

2 

4 

.324861 
.289297 
.257627 
.229423 
.204307 

13.2543 
11.8033 
10.5112 
9.3605 
8.3357 

12.9944 
11.5719 
10.3051 
9.1769 
8.1723 

14.7162 
13.1052 
11.6705 
10.3929 
9.2551 

13.9041 
12.3819 
11.0264 
9.8193 
8.7443 

5 
6 
7 
8 
9 

.181940 
.162023 
.144285 
.128490 
.114423 

7.4232 
6.6105 
5.8868 
5.2424 
4.6685 

7.2776 
6.4809 
5.7714 
5.1396 
4.5769 

8.2419 
7.3396 
6.5361 
5.8206 
5.1834 

7.7870 
6.9346 
6.1754 
5.4994 
4.8973 

10 
11 
19 

13 
14 

.101897 
.090742 
.080808 
.071962 
.064084 

4.1574 
3.7023 
3.2970 
2.9360 
2.6146 

4.0759 
3.6297 
3.2323 
2.8785 
2.5634 

4.6159 
4.1106 
3.6606 
3.2599 
2.9030 

4.3612 
3.8838 
3.4586 
3.0800 
2.7428 

15 
16 
17 
18 
19 

.057068 
.050821 
.045257 
.040303 
.035890 

2.3284 
2.0735 
1.8465 
1.6444 
1.4643 

2.2827 
2.0328 
1.8103 
1.6121 
1.4356 

2.5852 
2.3022 
2.0501 
1.8257 
1.6258 

2.4425 
2.1751 
1.9370 
1.7250 
1.5361 

20 
21 
22 
23 

24 

.031961 
.028462 
.025346 
.022572 
.020101 

1.3040 
1.1612 
1.0341 
.92094 
.82012 

1.2784 
1.1385 
1.0138 
.90288 
.80404 

1.4478 
1.2893 
1.1482 
1.0225 
.91058 

1.3679 
1.2182 
1.0848 
.96608 
.86032 

25 
26 
27 
28 
29 

.017900 
.015941 
.014195 
.012641 
.011257 

.73032 
.65039 
.57916 
.51575 
.45929 

.71600 
.63764 
.56780 
.50564 
.45028 

.81087 
.72213 
.64303 
.57264 
.50994 

.76612 
.68227 
.60755 
.54103 
.48180 

30 
31 
32 
33 
34 

.010025 
.008928 
.007950 
.007080 
.006305 

.40902 
.36426 
.32436 
.28886 
.25724 

.40100 
.35712 
.31800 
.28320 
.25220 

.45413 
.40444 
.36014 
.32072 

.28562 

.42907 
.38212 
.34026 
.30302 
.26985 

35 
36 

.005615 
.005000 

.22909 
.20400 

.22460 

.20000 

.25436 

.22650 

.24032 
.21400 

238                        NATIONAL  TUBE  COMPANY. 

WEIGHT    OF    PLATE    IRON    IN    POUNDS    PER 

LINEAL  FOOT. 

(Based  on  480  Ibs.  per  Cubic  Foot.    For  Steel  add  2  per  cent.) 

g  . 

THICKNESS  IN  INCHES. 

51 

T3  O 

M 

TV 

% 

ft 

X 

T5* 

X 

ft 

X 

12 

2.50 

5.00 

7.50 

10.00 

12.50 

15.00 

17.50 

20.00 

13 

2.71 

5.42 

8.13 

10.83 

13.54 

16.25 

18.96 

21.67 

14 

2.92 

5.83 

8.75 

11.67 

14.58 

17.50 

20.42 

23.33 

15 

3  13 

6.25 

9.38 

12.50 

15.63 

18.75 

21.88 

25.00 

16 

3.33 

6.67 

10.00 

13.33 

16.67 

20.00 

23.33 

26.67 

17 

3.54 

7.08 

10.63 

14.17 

17.71 

21.25 

24.79 

28.33 

18 

3.75 

7.50 

11.25 

15.00 

18.75 

22.50 

26.25 

30.00 

19 

3.96 

7.92 

11.87 

15.83 

19.79 

23.75 

27.71 

31.67 

20 

4.17 

8.33 

12.50 

18.67 

20.83 

25.00 

29.17 

33.33 

21 

4.38 

8.75 

13.13 

17.50 

21.88 

26.25 

30.63 

35.00 

22 

4.58 

9.17 

13.75 

18.33 

22.92 

27.50 

32.08 

36.67 

23 

4.79 

9.58 

14.38 

19.17 

23.96 

28.75 

33.54 

38.33 

24 

5.00 

10.00 

15.00 

20.00 

25.00 

30.00 

35.00 

40.00 

25 

5.21 

10.42 

15.  62120.83 

26.04 

31.25 

36.46 

41.67 

26 

5.42 

10.83 

16.25 

21.67 

27.08 

32.50 

37.92 

43.33 

27 

5.63 

11.25 

16.88 

22.50 

28.13 

33.75 

39.38 

45.00 

28 

5.83 

11.67 

17.50 

23.33 

29.17 

35.00 

40.83 

46.67 

29 

6.04 

12.08 

18.13 

24.17 

30.21 

36.25 

42.29 

48.33 

30 

6.25 

12.50 

18.75 

25.00 

31.25 

37.50 

43.75 

50.00 

32 

6.67 

13.33 

20.00 

26.67 

33.33 

40.00 

46.67 

53.33 

34 

7.08 

14.17 

21.25 

28.33 

35.42 

42.50 

49.58 

56.67 

36 

7.50 

15.00 

22.50 

30.00 

37.50 

45.00 

52.50 

60.00 

38 

7.92 

15.83 

23.75 

31.67 

39.59 

47.50 

55.42 

63.33 

40 

8.33 

16.67 

25.00 

33.33 

41.67 

50.00 

58.33 

66.67 

42 

8.75 

17.50 

26.25 

35.00 

43.75 

52.50 

61.25 

70.00 

44 

9.17 

18.33 

27.50 

36.67 

45.84 

55.00 

64.17 

73.33 

46 

9.58 

19.17 

28.75 

38.33 

47.92 

57.50 

67.08 

76.67 

48 

10.00 

20.00 

30.00 

40.00 

50.00 

60.00 

70.00 

80.00 

50 

10.42 

20.83 

31.25 

41.67 

52.08 

62.50 

72.91 

83.33 

52 

10.83 

21.67 

32.50 

43.33 

54.17 

65.00 

75.83 

86.67 

54 

11.25 

22.50 

33.75 

45.00 

56.25 

67.50 

78.75 

90.00 

56 

11.67 

23.33 

35.00 

46.67 

58.33 

70.00 

81.66 

93.33 

58 

12.08 

24.17 

36.25 

48.33 

60.42 

72.50 

84.58 

96.67 

60 

12.50 

25.00 

37.50 

50.00 

62.50 

75.00 

87.50 

100.00 

NATIONAL  TUBE  COMPANY.                       239 

WEIGHT    OF    PLATE    IRON    IN     POUNDS     PER 

LINEAL  FOOT 

(CONTINUED.) 

c  . 

ij 

THICKNESS  IN  INCHES. 

is 

r9* 

H 

H 

X 

H 

% 

if 

1 

12 

22.50 

25.00 

27.50 

30.00 

32.50 

35.00 

37.50 

40.00 

13 

24.38 

27.08 

29.79 

32.50 

35.21 

37.92 

40.63 

43.33 

14 

26.25 

29.17 

32.08 

35.00 

37.92 

40.83 

43.75 

46.67 

15 

28.13 

31.25 

34.38 

37.50 

40.63 

43.75 

46.88 

50.00 

16 

30.00 

33.33 

36.67 

40.00 

43.33 

46.67 

50.00 

53.33 

17 

31.88 

35.42 

38.96 

42.50 

46.05 

49.59 

53.13 

56.67 

18 

33.75 

37.50 

41.25 

45.00 

48.75 

52.50 

56.25 

60.00 

19 

35.67 

39.58 

43.54 

47.50 

51.45 

55.41 

59.37 

63.33 

20 

37.50 

41.67 

45.83 

50.00 

54.17 

58.33 

62.50 

66.67 

21 

39.38 

43.75 

48.13 

52.50 

56.88 

61.25 

65.63 

70.00 

22 

41.25 

45.83 

50.42 

55.00 

59.58 

64.17 

68.75 

73.33 

23 

43.13 

47.92 

52.71 

57.50 

62.30 

67.09 

71.88 

76.67 

24 

45.00 

50.00 

55.00 

60.00 

65.00 

70.00 

75.00 

80.00 

!     25 

46.88 

52.08 

57.29 

62.50 

67.70 

72.91 

78.13 

83.33 

26 

48.75 

54.17 

59.58 

65.00 

70.42 

75.83 

81.25 

86.67 

27 

50.63 

56.25 

61.88 

67.50 

73.13 

78.75 

84.38 

90.00 

28 

52.50 

58.33 

64.17 

70.00 

75.84 

81.67 

87.50 

93.33 

29 

54.38 

60.42 

66.46 

72.50 

78.55 

84.59 

90.63 

96.67 

30 

56.25 

62.50 

68.75 

75.00 

81.25 

87.50 

93.75 

100.0 

32 

60.00 

66.67 

73.33 

80.00 

86.67 

93.33 

100.0 

106.7 

34 

63.75 

70.83 

77.91 

85.00 

92.08 

99.17 

106.3 

113.3 

36 

67.50 

75.00 

82.50 

90.00 

97.50 

105.0 

112.5 

120.0 

38 

71.25 

79.17 

87.09 

95.00 

102.9 

110.8 

118.8 

126.7 

40 

75.00 

83.33 

91.67 

100.0 

108.3 

116.7 

125.0 

133.3 

42 

78.75 

87.50 

96.25 

105.0 

113.7 

122.5 

131.3 

140.0 

44 

82.50 

91.67 

100.8 

110.0 

119.2 

128.3 

137.5 

146.7 

46 

86.25 

95.83 

105.4 

115.0 

124.6 

134.2 

143.8 

153.3 

48 

90.00 

100.0 

110.0 

120.0 

130.0 

140.0 

150.0 

160.0 

50 

93.75 

104.2 

114.6 

125.0 

135.4 

145.8 

156.3 

166.7 

52 

97.50 

108.3 

119.2 

130.0 

140.8 

151.7 

162.5 

173.3 

54 

101.3 

112.5 

123.8 

135.0 

146.3 

157.5 

168.8 

180.0 

56 

105.0 

116.7 

128.3 

140.0 

151.7 

163.3 

175.0 

186.7 

58 

108.8 

120.8 

132.9 

145.0 

157.1 

169.2 

181.3 

193.3 

60 

112.5 

125.0 

137.5 

150.0 

162.5 

175.0 

187.5 

200.0 

-«; 

NATIONAL  TUBE  COMPANY. 


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NATIONAL  TUBE  COMPANY. 


STANDARD  SIZES  OF  SCREW-THREADS  FOR 
BOLTS  AND  TAPS. 

(CHAS.  A    BAUER.) 


1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

A 

• 

Z? 

d 

h 

/ 

D'-D 

D' 

d' 

H 

¥ 

20 

Inches 
.2608 

Inches 
.1&55 

Inches 
.0379 

Inches 
.0062 

Inches 
006 

Inches 
.2668 

Inches 
.1915 

Inches 
.2024 

18 

.3245 

.2403 

.0421 

.0070 

.006 

.3305 

.2463 

.2589 

% 

16 

.3885 

.2938 

.0474 

.0078 

.006 

.3945 

.2998 

.3139 

T5 

14 

.4530 

.3447 

.0541 

.0089 

.006 

.4590 

.3507 

.3670 

5/ 

13 

.5166 

.40CO 

.0582 

.0096 

.006 

.5226 

.4060 

.4236 

A 

12 

.5805 

.4543 

.0631 

.0104 

.007 

.5875 

.4613 

.4802 

a£ 

11 

.6447 

.5069 

.0689 

.0114 

.007 

.6517 

.5139 

.5346 

% 

10 

.7717 

.6201 

.0758 

.0125 

.007 

.7787 

.6271 

.6499 

9 

.8991 

.7307 

.0842 

.0139 

.007 

.9061 

.7377 

.7630 

l" 

8 

1.0271 

.8376 

.0947 

.0156 

.007 

1.0341 

.8446 

.8731 

7 

1.1559 

.9394 

.1083 

.0179 

.007 

1.1629 

.9464 

.9789 

1^4 

7 

1.2809 

1.0644 

.1083 

.0179 

.007 

1.2879 

1.0714 

1.1039 

A= nominal  diameter  of  bolt. 
Z?=actual  diameter  of  bolt. 

d= diameter  of  bolt  at  bottom  of  thread. 

w^number  of  threads  per  inch. 

/—flat  of  bottom  of  thread. 

^=depth  of  thread. 
D'  and  dTr=diameters  of  tap. 
//—diameter  of  hole  in  nut  before  tapping. 
,    .2165 


d=A  — 


1.29904 


.7577    D  —  c 


.125 


H=D'—- 

Efficiency  of  Screw-bolts.— Mr.  Lewis  gives  the  following 
approximate  formula  for  ordinary  screw-bolts  (V  threads, 
with  collars):  /=pitch  of  screw,  ^^outside  diameter  of 


(T                          °fc 

NATIONAL  TUBE  COMPANY.                      243     ' 

screw,  /''—force  applied  at  circumference  to  lift  a  unit  of 

weight,  E=  efficiency  of  screw.     For  an  average  case,  in 
which  the  coefficient  of  friction  may  be  assumed  at  0.15, 

F 

.    P  +  d            K        P 

'     3d 

'     P  + 

For  bolts  of  the  dimensions  given  above,  ^4-inch  pitch, 
and  outside  diameters  lj£,  2^4,  3%,    and  4^   in.,    the 

efficiencies  according  to  this  formula  would  be,  respec- 

tively, 0.25,  0.167,  0.125,  and  0.10. 

James  McBride  (Trans.  A.S.M.K.,  xii.  781)  describes  an 

experiment  with  an  ordinary  2-in.  screw-bolt,  with  a  V 

thread,  4^  threads  per  inch,  raising  a  weight  of  7500  Ibs., 
the  force  being  applied  by  turning  the  nut.  Of  the  power 
applied  89.8$  was  absorbed  by  friction  of  the  nut  on  its 
supporting  washer  and  of  the  threads  of  the  bolt  in  the 
nut.     The  nut  was  not  faced,  and  had  the  flat  side  to 

the  washer. 

STRENGTH  OF  WROUGHT  IRON  BOLTS. 

(COMPUTED  BY  A.   F.  NAGLE.) 

J 

1 

a 

o 

0 

Stress  upon  Bolt  upon  Basis 
of  working  strength  of 

• 

O 

W 
*$$ 

1 

If, 

a   « 

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Id 

Ig 

Id 

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is1 

S  5T 

s  g1 

0  $ 

8  g* 

eu 

a 

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PQ 

5 

3 

^ 

1-1 

" 

Q 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

X 

13 

.38 

.12 

350 

460 

580 

810 

1160 

5800 

T98 

12 

.44 

.15 

450 

600 

750 

1050 

1500 

7500 

% 

11 

.49 

.19 

560 

750 

930 

1310 

1870 

9000 

% 

10 

.60 

.28 

750 

1130 

1410 

1980 

2830 

14000 

% 

9 

.71 

.39 

1180 

1570 

1970 

2760 

3940 

19000 

1 

8 

.81 

.52 

1550 

2070 

2600 

3630 

5180 

25000 

ll^j 

7 

.91 

.65 

1950 

2600 

3250 

4560 

6510 

30000 

H 

7 

1.04 

.84 

2520 

3360 

4200 

5900 

8410 

39000 

% 

6 

.12 

1.00 

3000 

4000 

5000 

7000 

10000 

46000 

12 

6 

.25 

1.23 

3680 

4910 

6140 

8600 

12280 

56000 

% 

5^ 

.35 

1.44 

4300 

5740 

7180 

10000 

14360 

65000 

% 

5 

.45 

1.65 

4950 

6600 

8250 

11560 

16510 

74000 

]% 

5 

.57 

1.95 

5840 

7800 

9800 

13640 

19500 

85000 

2 

''  •• 

.66 

2.18 

6540 

8720 

10900 

15260 

21800 

95000 

2}4 

4'^ 

1.92 

2.88 

8650 

11530 

14400 

20180 

28800 

125000 

2J*<3 

4 

2.12 

3.55 

10640 

14200 

17730 

24830 

35500 

150000 

2% 

4 

2.37 

4.43 

13290 

17720 

22150 

31000 

44300 

186000 

3 

3Mj 

2.57 

5.20 

15580 

20770 

26000 

36360 

52000 

213000 

3^> 

3J4 

3.04 

7.25 

21760 

29000 

36260 

50760 

72500 

290000 

4  ~ 

3 

3.50 

9.62 

28860 

38500 

48100 

67350 

96200 

385000 

NATIONAL  TUBE  COMPANY. 


When  the  greatest  load  that  has  to  be  sustained  by  a 
bolt  is  known,  and  the  working  strength  per  sq.  in.  of 
the  material  constituting  it  is  determined,  look  in  the 
proper  column  for  the  given  load.  Should  the  load 
sought  be  not  found,  then  take  the  load  next  larger  as 
found  in  the  column,  and  opposite  to  it  in  the  first  col- 
umn read  the  required  size  of  bolt. 

Effect  of  Initial  Strain  in  Bolts. — Suppose  that  bolts  are 
used  to  connect  two  parts  of  a  machine  and  that  they  are 
screwed  up  tightly  before  the  effective  load  comes  on  the 
connected  parts.  Let  P^  =  the  initial  tension  on  a  bolt 
due  to  screwing  up,  and  Pa  =  the  load  afterwards  added. 
The  greatest  load  may  vary  but  little  from  Pl  or  P2, 
according  as  the  former  or  the  latter  is  greater,  or  it  may 
approach  the  value  P l  -f-  P2,  depending  upon  the  rela- 
tive rigidity  of  the  bolts  and  of  the  parts  connected. 
Where  rigid  flanges  are  bolted  together,  metal  to  metal, 
it  is  probable  that  the  extension  of  the  bolts  with  any 
additional  tension  relieves  the  initial  tension,  and  that 
the  total  tension  is  P x  or  P  2,  but  in  cases  where  elastic 
packing,  as  india  rubber,  is  interposed,  the  extension  of 
the  bolts  may  very  little  affect  the  initial  tension,  and 
the  total  strain  may  be  nearly  P ±  -j-  P2-  Since  the 
latter  assumption  is  more  unfavorable  to  the  resistance 
of  the  bolt,  this  contingency  should  usually  be  provided 
for.  (See  Unwin,  "  Elements  of  Machine  Design"  for 
demonstration.) 


WEIGHTS 

AND 

MEASURES, 


NATIONAL  TUBE  COMPANY. 


WEIGHTS  AND  MEASURES, 


AVOIRDUPOIS  OR  COMMERCIAL  WEIGHT. 


UNITED  STATES  AND  BRITISH. 


Grains. 

Ounces. 

Pounds. 

Hundred- 
weight. 

Gross  Tons. 

1. 

0.002286 

0.000143 

0.00000128 

0.000000176 

437.5 

1. 

0.0625 

0.00055804 

0.00002790 

7000. 

16. 

I. 

0.0089286 

0.0004464 

784000. 

1792. 

112. 

1. 

0.05 

5680000. 

35840. 

2240. 

20. 

1. 

1  pound  avoirdupois  =  1.215278  pounds  troy. 
1  net  ton  =  2000  pounds  =  0.892857  gross  tons. 
1  pound  troy  =  0.82286  pounds  avoirdupois. 


LINEAR  MEASURE. 


UNITED  STATES  AND  BRITISH. 


Inches. 

Feet. 

Yards. 

Rods. 

Miles. 

1. 

0.08333 

0.02778 

0.0050505 

0.00001578 

12. 

1. 

0.33333 

0.0606061 

0.00018939 

36. 

3. 

I. 

0.1818182 

0.00056818 

198. 

16.5 

5.5 

1. 

0.003125 

63360. 

5280. 

1760. 

320. 

1. 

GUNTER'S  CHAIN  MEASURE. 


USED  IN  SURVEYING. 

1  link    =  7.92  inches  =  0.01  chain  =  0.000125  mile. 

1  chain  =  100    links    =     66  feet    =  4  rods=0.0125  mile 

1  mile    =   80    chains  =  8000  links. 


NATIONAL  TUBE  COMPANY. 


SQUARE  OR  SURFACE  MEASURE, 


UNITED  STATES  AND  BRITISH. 


Square 
Inches. 

Square  Feet. 

Square  Yards 

Square 
Rods. 

Acres. 

Square 
Miles. 

0  006944 

0  0007716 

144 

o  linn 

1296 

g 

1. 

6.03306 

0.0002066 

39204 
6272640 

272.25 
43560. 
27878400. 

30.25 
4840. 
3097600. 

1. 
160. 
102400. 

0.00625 
1. 
640. 

6.00000977 
0.0015625 
1. 

1  acre  =  10  square  chains. 

CUBIC  MEASURE. 

1728  cubic  inches=l  cubic  foot, 
27  cubic  feet     =1  cubic  yard =46656  cubic  inches, 
1  cord  wood     =4  ft.  X  4  ft.  X 8  ft. =128  cubic  feet, 
1  perch  of  masonry=16.5  ft.Xl.5  ft.Xl  ft. =24. 75 
cubic  feet,  but  is  generally  assumed  to  be  25  cubic  feet. 

DRY  MEASURE. 


UNITED  STATES  ONLY. 


Struck 
Bush. 

Pecks. 

Quarts. 

Pints. 

Gallons. 

Cubic  Inch. 

1 

4 

32. 

64 

8. 

2150.4 

1 

8. 

16 

2. 

537.6 

1. 

2 

0.25 

67.2 

0.5 

1 

0.125 

33.6 

4. 

8 

1. 

268.8 

The  United  States  standard  unit  for  dry  measure  is  the 
old  English  Winchester  bushel,  which  contains  2,150.42 
cubic  inches,  or  1.2445  cubic  feet. 

The  heaped  bushel,  the  cone  of  which  is  6  inches 
above  the  brim  of  the  measure,  contains  2,747.7  cubic 
inches. 


NATIONAL  TUBE  COMPANY. 


In  New  York  a  bushel  contains  2,218. 2]cubic  inches,  or 
1.2837  cubic  feet,  which  is  the  same  as  the  Imperial 
bushel  of  England.  33  .English  or  Imperial  bushels  are 
equal  to  34.04  Winchester  or  United  States  bushels. 

LIQUID  MEASURE. 


UNITED  STATES  ONLY. 


Cubic  Inch. 

Pints. 

Quarts. 

Gallons. 

Barrels. 

Hogs- 
head. 

28.875 

1. 

0.5 

0.125 

0.003968 

57.75 

2. 

1. 

0.25 

0.007937 

231. 

8. 

4. 

1. 

0.031746 

7276.5 

252. 

126. 

31.5 

1. 

0.5 

14553.0 

504. 

252. 

63. 

2. 

1. 

The  British  Imperial  gallon  =  1.20032  U.  S.  gallons. 

The  United  States  standard  unit  for  liquid  measure  is 
the  gallon  =  231  cu.  in.  =  8.33888  pounds,  avoirdupois, 
of  distilled  water  at  62°  Fahr. 

The  English  standard  is  the  Imperial  gallon  =  277.2738 
cu.  in.  =  10  pounds,  avoirdupois,  of  distilled  water  at 
62°  Fahr. 

NAUTICAL  MEASURE. 

A  knot  or  nautical  mile  =  1.1527  statute  miles  =  6086. 
feet  =  length  of  a  minute  of  longitude  of  the  earth  at 
the  equator,  at  the  level  of  sea,  as  determined  by  U.  S. 
Coast  Survey. 

3  knots  =  1  league. 

SHIPPING  MEASURE. 

1  Register  ton  =  100  cubic  feet. 

1  U.  S.  Shipping  ton  =40  cubic  feet. 

1  British  Shipping  ton  =  42  cubic  feet. 


NATIONAL  TUBE  COMPANY. 


MEASURE  OF  WORK  AND  POWER. 

A  unit  of  work  =  one  foot  pound,  or  a  pressure  of  one 
pound  exerted  .through  a  space  of  one  foot. 
A  British  Thermal  unit  =  778  foot  pounds. 

f  33,000  foot  pounds  per  minute, 
550  foot  pounds  per  second, 

42.42  heat  units  per  minute. 
A  Horse  Power  =  4     Q  ?()7  heat  units  per  second> 

746  watts, 
I     0.746  kilowatt. 


THE  METRIC  SYSTEM  OF  WEIGHTS  AND 
MEASURES. 

In  the  Metric  System,  the  Meter  is  the  base  of  all  the 
weights  and  measures  which  it  employs. 

The  Meter  is  the  primary  unit  of  length  and  was  in- 
tended to  be  one-ten  millionth  part  of  the  distance, 
measured  on  a  meridian  of  the  earth,  from  the  equator 
to  the  pole,  and  equals  about  39.37  inches. 

Upon  the  Meter  are  based  the  following  primary  units; 
the  Square  Meter  the  Are,  the  Cubic  Meter  or  Stere  the 
Liter,  and  the  Gram. 

The  Square  Meter  or  Centare  is  the  unit  of  measure  for 
small  surfaces. 

The  Are  is  the  unit  of  land  measure  ;  this  is  a  square 
whose  side  is  ten  meters  in  length,  and  which  contains 
one  hundred  square  meters  or  centares. 

The  Cubic  Meter,  or  Stere,  is  the  unit  of  volume;  this  is 
a  cube  whose  edge  is  one  meter  in  length. 

The  Liter  is  the  unit  of  capacity  ;  this  is  the  capacity 
of  a  cube  whose  edge  is  one  tenth  of  a  meter,  that  is, 
one  decimeter  in  length. 

The  Gram  is  the  unit  of  weight ;  this  is  the  weight  of 
distilled  water  at  4°  centigrade,  contained  in  a  cube 
whose  edge  is  the  one  hundredth  part  of  a  meter. 

From  these  primary  units  the  higher  and  lower  orders 
of  units  are  derived  decimally  as  follows  : 


250 

NATIONAL  TUBE  COMPANY. 

Scheme  of  the  Weights  and  Measures  of  the  Metric  System. 

Ratios 

Lengths 

Surface 

5   Volumes 

Weights 

1,000,000. 

Millier,  or  Tonneau 

100  000 

Quintal 

10,000. 
1  000. 

Myr'iameter 
Kil'ometer 

Myr'iagram 

Kil'oliter 

100. 
10 

Hec'tometer 

Hect'are 

Hec'toliter 

Hec'togram 

I. 

Meter 

Are 

Ll'ter 

Gram 

0.1 

Dec'imeter 

Dec'iliter 

Dec'igram 

0.01 
0  001 

Cen'timeter 
Mil'limeter 

Cen'tare 

Cen'tiliter 
Mil'liliter 

Cen'tigram 

It  will 

be  seen,  from  this  table,  that  ten  millimeters 

equal  one 

centimeter,  ten  centimeters 

equal  one  deci- 

meter,  and  so  on. 

Multiples  and  sub-multiples  of  the 

units,   meter,  liter 

and  gram  are  expressed  by  the  prefixes  : 

Deka    =      10 

Deci  = 

=  0.1 

Hecto  =    100 

Centi  =  0.01 

Kilo     =  1000 

Milli  = 

=  0.001 

ABBREVIATIONS  COMMONLY  IN  USE. 

mm,    millimeter, 

m8,      square  meter, 

cm,     centimeter, 

km8 

4  '      kilometer, 

dm,     decimeter, 

mm3,  cubic  millimeter, 

m,        meter, 

cm3    ) 

"    centimeter, 

km,     kilc 

>meter. 

cc      f 

mm8,  square  millimeter, 

dm3, 

"     decimeter, 

cm8,        " 

centimeter, 

m3, 

"    meter, 

dm8,        ' 

a,  are  ; 

ha,  hectare  ;  cl,  centiliter  ;  1 

,  liter  ;  hi,  hecto- 

liter  ;  s,  stere  ;  mg,  milligram  ;  eg,  centigram  ;  g,  gram; 

kg,  kilo,  or  kilogram 

;  t,  tonneau,  or  metric  ton. 

NATIONAL  TUBE  COMPANY. 


METRIC  AND  U.  S.  CONVERSION  TABLE. 


MEASURES  OF  LENGTH. 
METRIC  TO  U.  S. 

1  millimeter  =    0.03937  inch. 
1  centimeter  =   0.3937      ." 
1  meter          =  39 . 37  inches. 
1      "  =   3.2808  feet. 

1  kilometer   =   0.6214  mile. 

U.  S.  TO  METRIC. 

1  inch  =25.4  millimeters. 
1     "      =2.54  centimeters. 
1     "     =    0.254  meter. 
1  foot  =    0.3048     " 
1  mile  =    1.609  kilometers. 

MEASURES  OF  SURFACE. 

METRIC  TO  U.  S. 

1  sq.  millimeter  =  0.00155  sq.  inch. 

1    "     centimeter  ==  0.155        "       " 
1    "    meter           =10.764        "    feet. 

1    "  =  1.196        "    yards. 

1  hectare  =  2.471  acres. 

1  =  0.00386  sq.  mile. 

1  sq.  kilometer    =  0.3861     " 

U.  S.  TO  METRIC. 

1  sq.  inch  =  645.14    sq.  millimeters. 

1     "      "     =         6.452    "    centimeters. 

1     "foot    =         0.0929"    meter. 

1     "yard   =          0.8361  " 

1         acre  =         0.4047  hectares. 

1  sq.  mile  =  259.00  " 

1     '       "     =         2.59    sq.  kilometers. 


NATIONAL  TUBE  COMPANY. 


MEASURES  OF  VOLUME  AND  CAPACITY. 

METRIC  TO  U.  S. 

1  cu.  centimeter  —    0.061  cu.  inch. 
1     "    meter  =35.316     "    feet. 

1     "  =    1.308     "    yards. 

1  liter  =  1  cu.  decimeter  =  61.023  cu.  inch. 

LIQUID  MEASURE. 

1  liter  =      1.0567  quart. 

1     "  =      0.2642  gallon. 

1  cubic  meter  =  264.17      gallons. 

DRY  MEASURE. 

1  liter  =0.908    quart. 

1  hectoliter  =  2.8375  bushels 

U.  S.  TO  METRIC. 

1  cu.  inch  =  16.39    cu.  centimeters. 
1     "    foot  =    0.0283  "    meter. 
1     "    yard  =    0.7645" 
1     "    foot  =  28.32  liters. 

LIQUID  MEASURE. 

1  quart  =  0.9463  liter. 
1  gallon  =  3.7854  liters. 
1  "  =  0.0038  cu.  meter. 

DRY  MEASURE. 

1  quart     =  1.1013  litres. 

1  bushel  =  0.3524  hectoliter. 

WEIGHTS. 

METRIC  TO  U.  S. 

1  milligram    =    0.0154  grain. 

1  gram  =  15.432    grains. 

1  kilogram      =    2.2046  Ibs.  (avoir.) 

1  metric  ton  =    1.1023  net  tons. 
1       "  "   =    0.9842  gross  ton. 

U.  S.  TO  METRIC. 

1  grain  =  64.80      milligrams. 

1      "  =    0.0648  gram. 

1  Ib.  (avoir.)  =    0.4536  kilogram. 
1  net  ton        =    0.9076  metric  ton. 
1  gross  ton    =    1.0161        "      tons. 


NATIONAL  TUBE  COMPANY. 


COMPOUND  UNITS. 

METRIC  TO  UNITED   STATES. 

1  kilogram  per  meter  =  0.6720  Ibs.  per  foot. 

1  kilogram  per  sq.  centimeter— 14.223    Ibs.  per  sq.  inch. 
1  kilogram  per  sq.  meter          =  0.2048  Ibs.  per  sq.  foot. 

kilogram  per  cubic  meter     =  0 . 0624  Ibs.  per  cubic  ft. 

kilogram-meter  =  7.233    footpounds. 

chevel  vapeur  (metric  H.  P.)=  0.986    horse-power. 

kilo,  watt  =1.340 

kilo,  per  chevel  =  2.235    Ibs.  per  H.  P. 

UNITED  STATES  TO  METRIC. 

1  Ib.  per  foot  =  1.4882  kilograms  per  meter. 

1  Ib.   per  sq.  inch  =  0.0703  kilo,  per  sq.  centimeter. 

1  Ib.  per  sq.  foot  =  4.8825  kilograms  per  sq.  meter. 

1  Ib.  per  cubic  foot  =16.0192  kilo,  per  cubic  meter. 

1  footpound  =  0.1383  kilogram-meter  % 

1  horse-power  =  1.014   che vel  vapeur  (metric  H.  P.) 

1         "         "  =0.746    kilo  watt. 

1  Ib.  per  horse-power  =  0.447    kilos  per  chevel. 

HEAT  INTENSITY. 

Temp.  Centigrade  =  (temp.  Fahr.  —  32° W 

9  \ 

Temp.  Fahrenheit  =  (temp.  C.  X  5"  7+  32°. 

HEAT   QUANTITY. 

A  kilogram  calorie  =3.968   British  thermal  units. 

A  pound  calorie  =1.8  "  " 

A  British  thermal  unit  =  0.252  kilogram  calorie 
A  British  thermal  unit  =  0.555  pound  calorie. 


fir                                      "^ 

254                      NATIONAL  TUBE  COMPANY. 

MECHANICAL,   ELECTRICAL   AND    HEAT 

EQUIVALENTS. 

(H.  W.  LEONARD.) 

UNIT. 

EQUIVALENT  VALUE  IN  OTHER  UNITS 

1,000  watt  hours. 

1  .  34  horse-power  hours  . 

2,654,200  ft.-lbs. 

3,600,000  joules. 

3,  412  heat  units. 

1 
K.  W. 

367,000  kilogram  metres. 

Hour  = 

0.235  Ib.  carbon  oxidized  with  perfect 

efficiency. 

3.53  Ibs.  water  evaporated  from  and  at 

212°  F. 

22.75  Ibs.  of  water  raised  from  62°  to 

212°  F. 

0.746  K.  W.  hours. 

1,980,000  ft.-lbs. 

2,545  heat-units. 

273,740k.  g.  m. 

1 
H   P 

0.175  Ib.  carbon  oxidized  with  perfect 

Hour  = 

efficiency. 

2  .  64  Ibs.  water  evaporated  from  and  at 

212°  F. 

17.0  Ibs.  water  raised  from  62°   F.    to 

212°  F. 

1,000  watts. 

1  .  34  horse-power  . 

2,654,200  ft.-lbs.  per  hour. 

44,240  ft.-lbs.  per  minute. 

1 
Kilowatt 

737.  3  ft.-lbs.  per  second. 
3,412  heat-units  per  hour. 

56.9  heat-units  per  minute. 

0.948  heat-unit  per  second. 

0.2275  Ib.  carbon  oxidized  per  hour. 

3.53  Ibs.  water  evaporated  per  hour 

from  and  at  212°  F. 

NATIONAL  TUBE  COMPANY.                      255 

MECHANICAL,   ELECTRICAL   AND   HEAT 
EQUIVALENTS.—  (CONTINUED). 

UNIT. 

EQUIVALENT  VALUE  IN  OTHER  UNITS 

1 

H.  P.  = 

746  watts. 
0.746  K.  W. 
33,000  ft.-lbs.  per  minute. 
550  ft.-lbs.  per  second. 
2,545  heat-units  per  hour. 
42.4  heat-units  per  minute. 
0.707  heat  units  per  second. 
0.175  Ibs.  carbon  oxidized  per  hour. 
2.64  Ibs.  water  evaporated  per  hour  from 
and  at  212°  F. 

1 

Joule  = 

1  watt  second  . 
0.000000278  K.  W.  hour. 
0.102k.  g.  m. 
0.0009477  heat-  units. 
0.7878  ft.  -Ib. 

1 
Ft.-lb. 

1.356  joules. 
0.1383k.  g.  m. 
0.000000377  K.  W.  hours. 
0.001285  heat-units. 
0.  0000005  H.  P.  hour. 

1 

Watt  = 

1  joule  per  second. 
0.  00134  H.  P. 
3.412  heat-units  per  hour. 
0.7373ft.-lb.  per  second. 
0.0035  Ib.  water  evaporated  per  hour. 
44.24  ft.-lbs.  per  minute. 

1  Watt 
per  sq. 

in.  = 

8.19  heat-units  per  square  foot  per  minute. 
6371  ft.-lbs.  per  square  foot  per  minute. 
0.193  H.  P.  per  square  foot. 

X        ? 

A-  «£ 

256                     NATIONAL  TUBE  COMPANY. 

MECHANICAL,   ELECTRICAL   AND  HEAT 
EQUIVALENTS.—  (CONTINUED). 

UNIT. 

EQUIVALENT  VALUE  IN  OTHER  UNITS. 

1 
Heat 
unit. 

1,055  watt  seconds. 
778ft.-lbs. 
107.6  kilogram  metres. 
0.  000293  K.  W.  hour. 
0.  000393  H.  P.  hour. 
0.0000688  Ib.  carbon  oxidized. 
0.001036  Ib.  water    evaporated   from 
and  at  212°  F. 

1  Heat- 
unit,  per 
Sq.ft.  per 
min.  = 

0.122  watt  per  square  inch. 
0.0176  K.  W.  per  square  foot. 
0.0236  H.  P.  per  square  foot. 

1  Kilog- 
gram 
Metre  = 

7.888  ft.-lbs. 

0.  00000365  H.  P.  hour. 
0.  00000272  K.  W.  hour. 
0.0093  heat-units. 

lib. 
Carbon 
Oxidized 
with 
perfect 
Efficiency 

14,544  heat-units. 
1.11  Ib.  Anthracite  coal  oxidized. 
2.5  Ibs.  dry  wood  oxidized. 
21  cubic  feet  illuminating-gas. 
4.26  K.  W.  hours. 
5.71  H.  P.  hours. 
11,315,000  ft.-lbs. 
15  Ibs.  of  water  evaporated  from  and 
at  212°  F. 

1  Ib. 
Water 
Evapor- 
ted  from 
and  at 
212°  F.= 

0.283  K.  W.  hour. 
0.379H.  P.  hour. 
965.  7  heat-units. 
103,900k.  g.  m. 
1,019,000  joules. 
751,300  ft.-lbs. 
0.0664  Ib.  of  carbon  oxidized. 

?• 

MENSURATION, 

TRIGONOMETRY 

AND 

MATHEMATICAL  TABLES. 


NATIONAL  TUBE  COMPANY. 


MENSURATION,  TRIGONOMETRY  AND 
MATHEMATICAL  TABLES. 


MENSURATION. 


MENSURATION  OF  SURFACES. 

Area  of  any  parallelogram  =  base  X  perpendicular 
height.  . 

"     "     "      triangle =  base  X  K   perpendicular 

height. 

"     "     "      circle =  (diameter)2  X  (0.7854,  or 

approx.  11/14.) 

"     "     sector  of  circle =  arc  X  1/2  radius. 

"  "  segment  of  circle  .  —  area  of  sector  of  equal 
radius  and  arc  less  area 
of  triangle. 

"     "    parabola =  base  X  2/3  height. 

"  "  ellipse =  longest  diameter  X  short- 
est diameter  X  0.7854. 

"     "     cycloid =  area  of  generating  circle 

X3. 

"  "  any  regular  polygon  =  sum  of  its  sides  X  per- 
pendicular from  its  cen- 
ter to  one  of  its  sides  -r-  2. 

Surface  of  cylinder =  area     of    both    ends    -f- 

(length  X  circumference.) 

"  •'  cone =  area  of  base  +  (circum- 
ference of  base  X  ^  slant 
height.) 

"       "    sphere =  (diameter)8  X  (3. 1416,  or 

approx.  22/7.) 

"       "    frustum =  (sum  of  girt  at  both  ends 

X  K  slant  height)  -f  area 
of  both  ends. 


NATIONAL  TUBE  COMPANY. 


Surface  of  cylindrical  ring  =  thickness  of  ring  added 
to  the  inner  diameter  X 
by  the  thickness X  9. 8698. 

"       "    segment =  height  of  segment  X  by 

whole  circumference  of 
sphere  of  which  it  is  a 
part. 

AREA  OF  AN  IRREGULAR  PLANE  SURFACE. 

Divide  the  surface 
into  any  number  of 
parallel  strips  of 
equal  widths,  "d." 
Take  the  sum  of  the 
—  middle  ordinates  hl5 
hs,  etc.,  to  hn,  in- 
clusive ;  then  the  sum  of  these  middle  ordinates,  multi- 
plied by  "  d  "  will  give  the  area  required. 

The  result,  of  course,  is  only  approximate,  the  close- 
ness of  the  approximation  depending  upon  the  number 
of  strips  into  which  the  surface  is  divided. 

Any  degree  of  accuracy  desired  may  be  attained  by 
making  the  number  of  strips  sufficiently  numerous.  In 
practice  it  is  usually  best  to  determine  the  area  of  an 
irregular  figure  by  the  use  of  a  planimeter,  an  instrument 
especially  designed  for  measuring  areas  of  plane  figures. 

REGULAR  POLYGONS. 

1.  To  find  the  area  of  any  regular  polygon.     Square 
one  of  its  sides,  and  multiply  this  square  by  the  corres- 
ponding number  in  the  third  column  of  the  following  table. 

2.  Having  a  side  of  a  regular  polygon,  to  find  the 
radius  of  a  circumscribing  circle.     Multiply  the  side  by 
the  corresponding  number  in  the  fourth  column. 

3.  Having  the  radius  of  a  circumscribing  circle,  to 
find  the  side  of  the  inscribed  regular  polygon.     Multiply 
the  radius  by   the  corresponding  number  in  the  fifth 
column. 


NATIONAL  TUBE  COMPANY. 


TABLE  OF  REGULAR  POLYGONS. 


1 

Angle 

CO 

Name  of 

Area  — 

Radius 

Side  = 

contained 

"o 

Polygon. 

S2X 

=  SX 

Rx 

between 

6 

two  sides. 

3 

/  Equilateral  \ 
I     triangle     / 

.433 

.5774 

1.732 

60° 

4 

Square 

1. 

.7071 

1.4142 

90° 

5 

Pentagon 

1.7205 

.8507 

1.1756 

108° 

6 

Hexagon 

2.5891 

1. 

1. 

120° 

7 

Heptagon 

3.6339 

1.1524 

.8678 

128.57° 

8 

Octagon 

4.8284 

1.3066 

.7654 

135° 

9 

Nonagon 

6.1818 

1.4619 

.684 

140° 

10 

Decagon 

7.6942 

1.618 

.618 

144° 

11 

Undecagon 

9.3656 

1.7747 

.5635 

147.27° 

12 

Dodecagon 

11.1962 

1.9319 

.5176 

150° 

In  the  above  table  S  =  side  of  polygon  and  R  =  radius 
of  circumscribing  circle. 


PROPERTIES  OF  THE  CIRCLE. 

Diameter      X  3.1416  =  circumference. 

"  X  0.8862  =  side  of  an  equivalent  square. 

"  X  0.7071  =  side  of  an  inscribed  square. 

(Diameter)3  X  0.7854  =  area  of  circle. 
Radius          X  6.2832  =  circumference. 
Circumference  -f-  3.1416  =  diameter. 

The  circle  contains  a  greater  area  than  any  plane 
figure,  bounded  by  an  equal  perimeter,  or  outline. 

The  areas  of  circles  are  to  each  other  as  the  squares  of 
their  diameter,  radii  or  circumferences.  Thus,  a  circle 
whose  diameter  is  double  that  of  another  has  four  times 
the  area  of  the  other. 


NATIONAL  TUBE  COMPANY 


VOLUMES  OF  SOLIDS. 

Vol.  of  Cylinder =  area  of  one  end  X  length. 

"     "  Sphere =  cube  of  diameter  X  0.5236. 

"  "  Segment  of  sphere  .  —  (cube  of  the  height  -j- 
three  times  the  square  of 
radius  of  base  X  height)  X 
0.5236. 

"  "  Cone  or  pyramid. . .  =  area  of  base  X  %  perpen- 
dicular height. 

*'  "  Frustum  of  cone. ..  =  (product  of  diameter  of 
both  ends  -j-  sum  of  their 
squares)  X  perpendicular 
height  X  0.2618. 

"  "  Frustum  of  pyramid^  (sum  of  the  areas  of  the 
two  ends  -J-  square  root  of 
their  product)  X  by  %  of 
the  perpendicular  height. 

' '  "  Wedge =  area  of  base  X  %  perpen- 
dicular height. 

"  '*  Frustum  of  wedge. .  =  %  perpendicular  height  X 
sum  of  the  areas  of  the 
two  ends. 

"  "  Ring =  (thickness  -f-  inner  dia- 
meter) X  square  of  the 
thickness  X  2.4674. 


NATIONAL  TUBE  COMPANY. 


TRIGONOMETRICAL  FORMULAE. 

EH 

Sine  of    Angle    E  A  H     =     

A  E 


J}    Cosine 


Cosecant 


AH 
A  E 
EH 
AH 
A  H 
EE[ 
E  A 
AH 
E  A 
EH 


TRIGONOMETRICAL  EQUIVALENTS. 


Sin     = 
Sin     = 


cot 


Cos    =     V  1  —sin2 

sin 
Cos    = 

tan 

Cos    =     sin  X  cot 
sin 


Cot        = 


Cot        = 


Sec        = 


Cosec    = 


cos 

sin 

1 
tan 

1 
cos 

1 


Tan    = 


Tan    = 


cos 

1 

cot 


Vers  =1  —  cos 
Covers  =  1  —  sin 
Sin2  +  cos2  =  1 


NATIONAL  TUBE  COMPANY. 


FUNCTIONS  OF  SUM  AND  DIFFERENCE  OF 
TWO  ANGLES. 

Sin  (x  -}-  y)  =  sin  x  cos  y  +  cos  x  sin  y 
Sin  (x  —  y)  =  sin  x  cos  y  —  cos  x  sin  y 
Cos  (x  -f-  y)  =  cos  x  cos  y  —  sin  x  sin  y 
Cos  (x  —  y)  =  cos  x  cos  y  -j-  s^n  x  si*1  7 
tan  x  -|-  tan  y 

all(X     ~T     y)       —          1       {an       x       £an       y 

tan  x  —  tan  y 


Tan  (x  —  y)  = 


1  +  tan  x  tan  y 
cot  x  cot  y  —  1 
cot  x  -|-  cot  y 
cot  x  cot  y  -f-  1 
cot  y  —  cot  x 


FUNCTIONS  OF  HALF  AN  ANGLE. 
Sin  K  z  =  +  4/1~2COSZ 

Tan  %  z  =  +  .i/1-0052 
—  V   1  - 


SUMS  AND  DIFFERENCES  OF  FUNCTIONS. 

Sin  (x  +  y)  +  sin  (x  —  y)  =  2  sin  x  cos  y 
Sin  (x  +  y)  —  sin  (x  —  y)  =  2  cos  x  sin  y 
Cos  (x  +  y)  -}-  cos  (x  —  y)  =  2  cos  x  cos  y 
Cos  (x  —  y)  —  cos  (x  -f-  y)  =  2  sin  x  sin  y 


NATIONAL  TUBE  COMPANY. 


Then  by  making  (x  -f  y)  =  A  and  (x  —  y)  =  B,  we 
have  x  =  %  (A  -j-  B)  and  y  =  yz  (A  —  B),  whence— 

Sin  A  +  sin  B  =  2  sin  %  (A  -f  B)  cos  ^  (A  —  B) 
Sin  A  —  sin  B  =  2  cos  %  (A  -f  B)  sin  %  (A  —  B) 
Cos  A  -f  cos  B  =  2  cos  %  (A  -f  B)  cos  ^  (A  —  B) 
Cos  A  —  cos  B  =  2  sin  %  (A  -j-  B)  sin  %  (A  —  B) 

Sin  A  -f  sin  B     _     tan  ^  (A  +  B) 

Sin  A  —  sin  B     "  " 


Cos  A  +  cos  B     _ 
Cos  A  —  cos  B     "  ' 


tan 
cot 


(A  —  B) 

(A  +  B) 


(A  —  B) 


SOLUTION  OF  RIGHT  TRIANGLE. 


Given  A  and  c,  to  find  B,  a  and  b. 

B  =  90°  —  A  ;    A  =  c  sin  A  ;    b  =  c  cos  A. 

Given  A  and  a,  to  find  B,  b  and  c. 


B  =  90°  —  A  ;  b  =  a  cot  A  ;  c  =  ^-^  . 

Given  A  and  b,  to  find  B,  a  and  c. 
B  =  90->_A;  a  =  btanA;c  =  ^- 

Given  c  and  a,  to  find  A,  B  and  b. 
Sin  A  =  ~  ;  B  =  90°  —  A  ;  b  =  a  cot  A. 

Given  a  and  b,  to  find  A,  B  and  c. 


TanA=;-;    B  =  90°  —  A  ;    c  = 


a 
sin  A' 


NATIONAL  TUBE  COMPANY. 


SOLUTION  OF  OBLIQUE  TRIANGLE. 


LAW  OF*  SINES, 
sin  A  b 


sin  B' 


sin  B 
sinC' 


sin  A 
sin~C 


LAW  OF  COSINES. 

a3  =  b2  +  c2  —  2  b  c  cos  A 
b2  =  a2  -{-  c8  —  2  a  c  cos  B 
c2  a  a2  -|-  b2  —  2  a  b  cos  C 


LAW  OF  TANGENTS. 
a  —  b     .__     tan  %  (A  —  B) 


a  +  b 

a  —  c 

a  +  c 

b  —  c 


tan 
tan 


(A  +  B) 
(A  —  C) 


(A  +  C) 

(B  —  C) 
tan  %  (B  +  C) 


tan 
tan 


Given  a,  A  and  B,  to  find  C,  b  and  c. 


=  180° 


a  sin  B 


a  sin  C 


Given  a,  b  and  A,  to  find  B,  C  and  c. 

b  sin  A  a  sin  C 

Sin  B  =  —      —  ;  C  =  180°  —  (A  +  B);  c  =  • 


NATIONAL  TUBE  COMPANY. 


Given  a,  b  and  C,  to  find  A,  B  and  c. 


b  sin  C  a  sin  C  *  /TiTT*       «     v        r\ 

c  =  — : ,  or  = — . ,  or  =A/  a-  +  b2  — 2  a  bcosC. 

sin  B  sin  A 

Given  a,  b  and  c,  to  find  A,  B  and  C . 


Sin  K  A  =j/(S  ~  b)  (S  ~*C);  in  which  S  =  %  (a+b+c); 
b  c 


Sin 


ab 


a  b 


Tan  %  B  =  ,/(S  —  a)  (S  —  C). 

V     s(s-b)   ' 


AREA  OF  A  TRIANGLE. 

Area  =  J^  a  c  sin  B,  that  is,  the  area  of  a  triangle 
equals  ^  the  product  of  two  sides  multiplied  by  the  sine 
of  the  included  angle. 


Also  area  =|/S  (8  —  a)  (S  —  b)  (  S  —  c); 
Where  S  =  %  (a  -f-  b  +  c). 


NATIONAL  TUBE  COMPANY.                     267       ' 

MATHEMATICAL  TABLES. 

1 

SINE. 

89 

88 
87 
86 

85 

0' 

10' 

20' 

30' 

40' 

50' 

60' 

0 

i 

2 

3 

4 

0.00000 
0.01745 
0.03490 
0.05234 
0.06976 

0.00291 
0.02036 
0.03781 
0.05524 
0.07266 

0.00582 
0  02327 
0.04071 
0.05814 
0.07556 

0.00873 
0.02618 
0.04362 
0.06105 
0.07846 

0.01164 
0.02908 
0.04653 
0.06395 
0.08136 

0.01454 
0.03199 
0.04943 
0.06685 
0.08426 

0.01745 
0.08490 
0.05234 
0.06976 
0.08716 

5 
0 

8 
9 

0.08716 
0.10453 
0.12187 
0.13917 
0.15643 

0.09005 
0.10742 
0.12476 
0.14205 
0.15931 

0.09295 
0.11031 
0.12764 
0.14493 
0.16218 

0.09585 
0.11320 
0.13053 
0.14781 
0.16505 

0.09874 
0.11609 
0.13341 
0.15069 
0.16792 

0.10164 
0.11898 
0.13629 
0.15356 
0  .  17078 

0.10453 
0.12187 
0.13917 
0.15643 
0.17365 

84 
83 
82 
81 
80 

10 
11 
12 
13 
14 

0.17365 
0.19081 
0.20791 
0.22495 
0.24192 

0.17651 
0.19366 
0.21076 
0.22778 
0.24474 

0.17937 
0.19652 
0.21360 
0.23062 
0.24756 

0.18224 
0.19937 
0.21644 
0.23345 
0.25038 

0.18509 
0.20222 
0.21928 
0.2362? 
0.25320 

0.18795 
0.20507 
0.22212 
0.23910 
0.25601 

0.19081 
0.20791 
0.22495 
0.24192 
0.25882 

79 

78 
77 
76 
75 

15 
16 
17 
18 
19 

0.25882 
0.27564 
0.29237 
0.30902 
0.32557 

0.26163 
0.27843 
0.29515 
0.31178 
0.32832 

0.26443 
0.28123 
0.29793 
0.31454 
0.33106 

0.26724 
0.28402 
0.30071 
0.31730 
0.33381 

0.27004 
0.28680 
0.30348 
0.32006 
0.33655 

0.27284 
0.28959 
0.30625 
0.32282 
0.33929 

0.27564 
0.29237 
0.30902 
0.32557 
0.34202 

74 
73 
72 
71 
70 

20 
21 
22 
23 
24 

0.34202 
0.35837 
0.37461 
0.39073 
0.40674 

0.34475 
0.36108 
0.37730 
0.39341 
0.40939 

0.34748 
0.36379 
0.37999 
0.39608 
0.41204 

0.35021 
0.36650 
0.38268 
0.39875 
0.41469 

0.35293 
0.36921 
0.3853? 
0.40142 
0.41734 

0.35565 
0.37191 
0.38805 
0.40408 
0.41998 

0  35837 
0.37461 
0.39073 
0.40674 
0.42262 

69 
68 
67- 
66 
65 

25 
26 

27 
28 
29 

0.42262 
0.43837 
0.45399 
0.46947 
0.48481 

0.42525 
0.44098 
0.45658 
0.47204 
0.48735 

0.42788 
0.44359 
0.45917 
0.47460 
0.48989 

0.43051 
0.44620 
0.46175 
0.47716 
0.49242 

0.43313 

0.44880 
0.46433 
0.47971 
0.49495 

0.43575 
0.45140 
0.46690 
0.48226 
0.49748 

0.43837 
0.45399 
0.46947 
0.48481 
0.50000 

64 
63 
62 
61 
60 

30 
31 
32 
33 
34 

'0.50000 
0.51504 
0.52992 
0.54464 
0.55919 

0.50252 
0.51753 
0.53238 
0.54708 
0.56160 

0.50503 
0.52002 
0.53484 
0.54951 
0.56401 

0.50754 
0.52250 
0.53730 
0.55194 
0.56641 

0.51004 
0.52498 
0.53975 
0.55436 

0.56880 

0.51254 
0.52745 
0.54220 
0.55678 
0.57119 

0.51504 
0.52992 
0.54464 
0.55919 
0.57358 

59 
58 
57 
56 
55 

35 
36 
37 
38 
39 

0.57358 
0.58779 
0.60182 
0.61566 
0.62932 

0.57596 
0.59014 
0.60414 
0.61795 
0.63158 

0.57833 
0.59248 
0.60645 
0.62024 
0.63383 

0.58070 
0.59482 
0.60876 
0.62251 
0.63608 

0.58307 
0.59716 
0.61107 
0.62479 
0.63832 

0.58543 
0.59949 
0.61837 
0.62706 
0.64056 

0.58779 
0.60182 
0.61566 
0.62932 
0.64279 

54 
53 
52 
51 
50 

40 
41 
42 
43 

44 

0.64279 
0.65606 
0.66913 
0.68200 
0.69466 

0  64501 
0.658-25 
0.67129 
0.68412 
0.69675 

0.64723 
0.66044 
0.67344 
0.68624 
0.69883 

0.64945 
0.66262 
0.67559 
0.68835 
0.70091 

0.65166 
0.66480 
0.67773 
0.69046 
0.70298 

0.65386 
0.66697 
0.67987 
0.69256 
0.70505 

0.  65606 
0.66913 
0.68200 
0.69466 
0.70711 

49 
48 
47 
46 
45 

i  ^  

60' 

60' 

40' 

30' 

20' 

10' 

0' 

COSINE 

268                      NATIONAL  TUBE  COMPANY. 

MATHEMATICAL  TABLES,  (CONTINUED.) 

1 

COSINE. 

Q 

0' 

10' 

20' 

30' 

40' 

50' 

60' 

0 

1.00000 

1.00000 

0.9999 

0.9999 

0.9999C 

0.9998 

0.99985 

89 

1 

0.99985 

0.99979 

0.9997 

0.99966 

0.99956 

0.9994 

0.99939 

88 

2 

0.99939 

0.99929 

0.9991 

0.99905 

0.9989S 

0.9987 

0.99863 

87 

3 

0.99863 

0.99847 

0.9983 

0.99813 

0.99795 

0.9977 

0.99756 

86 

4 

0.99756 

0.99736 

0.99714 

0.99692 

0.9966S 

0.9964 

0.99619 

85 

5 

0.99619 

0.99594 

0.99567 

0.99540 

0.99511 

0.99482 

0.99452 

84 

6 

0.99452 

0.99421 

0.99390 

0.99357 

0.99324 

0.99290 

0.99255 

83 

7 

0.99255 

0.99219 

0.99182 

0.99144 

0.99106 

0.99067 

0.99027 

82 

8 

0.99027 

0.98986 

0.98944 

0.98902 

0.98858 

0.98814 

0.98769 

81 

9 

0.98769 

0.98723 

0.98676 

0.98629 

0.98580 

0.98531 

0.98481 

80 

10 

0.98481 

0.98430 

0.98378 

0.98325 

0.98272 

0.98218 

0.98163 

79 

11 

0.98163 

0.98107 

0.98050 

0.97992 

0.97934 

0.97875 

0.97815 

78 

12 

0.97815 

0.97754 

0.97692 

0.97630 

0.97566 

0.97502 

0.97437 

77 

13 

0.97437 

0.97371 

0.97304 

0.97237 

0.97169 

0.97100 

0.97030 

76 

14 

0.97030 

0.96959 

0.96887 

0.96815 

0.96742 

0.96667 

0.96593 

75 

15 

0.96593 

0.96517 

0.96440 

0.96363 

0.96285 

0.96206 

0.96126 

74 

16 

0.96126 

0.96046 

0.95964 

0.95882 

0.95799 

0.95715 

0.95630 

73 

17 

0.95630 

0.95545 

0.95459 

0.95372 

0.95284 

0.95195 

0.95106 

72 

18 

0.95106 

0.95015 

0.94924 

0.94832 

0.94740 

0.94646 

0.94552 

71 

19 

0.94552 

0.94457 

0.94361 

0.94264 

0.94167 

0.94068 

0.93969 

70 

20 

0.93969 

0.93869 

0.93769 

0.93667 

0.93565 

0.93462 

0.93358 

69 

21 

0.93358 

0.93253 

0.93148 

0.93042 

0.92935 

0.92827 

0.92718 

68 

22 

0.92718 

0.92609 

0.92499 

0.92388 

0.92276 

0.92164 

0.92050 

67 

23 

0.92050 

0.91936 

0.91822 

0.91706 

0.91590 

0.91472 

0.91355 

66 

24 

0.91355 

0.91236 

0.91116 

0.90996 

0.90875 

0.90753 

0.90631 

65 

25 

0.90631 

0.90507 

0.90383 

0.90259 

0.90133 

0.90007 

0.89879 

64 

26 

0.89879 

0.89752 

0.89623 

0.89493 

0.89363 

0.89232 

0.89101 

63 

27 

0.89101 

0.88968 

0.88835 

0.88701 

0.88566 

0.88431 

0.88295 

62 

28 

0.88295 

0.88158 

0.88020 

0.87882 

0.87743 

0.87603 

0.87462 

61 

29 

0.87462 

0.87321 

0.87178 

0.87036 

0.86892 

0.86748 

0.86603 

60 

"  30 

0.86603 

0.86457 

0.86310 

0.86163 

0.86015 

0.85866 

0.85717 

59 

31 

0.85717 

0.85567 

0.85416 

0.85264 

0.85112 

0.84959 

0.84805 

58 

32 

0.84805 

0.84650 

0.84495 

0.84339 

0.84182 

0.84025 

0.83867 

57 

33 

0.83867 

0.83708 

0.83549 

0.83389 

0.83228 

0.83066 

0.82904 

56 

34 

0.82904 

0.82741 

0.82577 

0.82413 

0.82248 

0.82082 

0.81915 

55 

35 

0.81915 

0.81748 

0.81580 

0.81412 

0.81242 

0.81072 

0.80902 

54 

36 

0.80902 

0.80730 

0.80558 

0.80386 

0.80212 

0.80038 

0.79864 

53 

37 

0.79864 

0.79688 

0.79512 

0.79335 

0.79158 

0.78980 

0.78801 

52 

38 

0.78801 

0.78622 

0.78442 

0.78261 

0.78079 

0.77897 

0.77715 

51 

39 

0.77715 

0.77531 

0.77347 

0.77162 

0.76977 

0.76791 

0.76604 

50 

40 

0.76604 

0.76417 

0.76229 

0.76041 

0.75851 

0.75661 

0.75471 

49 

41 

0.75471 

0.75280 

0  75088 

0.74896 

0.74703 

0.74509 

0.74314 

48 

42 

0.74314 

0.74120 

0.73924 

0.73728 

0.73531 

0.73333 

0.73135 

47 

43 

0.73135 

0.72937 

0.72737 

0.72537 

0.72*37 

0.72136 

0.71934 

46 

44 

0.71934 

0.71732 

0.71529 

0.71325 

0.71121 

0.70916 

0.70711 

45 

60' 

50' 

40' 

30' 

20' 

10' 

0' 

I 

SINE. 

1 

NATIONAL  TUBE  COMPANY.                      269 

MATHEMATICAL  TABLES.  (CONTINUED.) 

i 

TANGENT. 

I 

0' 

10' 

20' 

30' 

40' 

w 

60' 

0 

0.00000 

0.00291 

0.00582 

0.00873 

0.01164 

0.01455 

0.01746 

89 

1 

0.01746 

0.02036 

0.02328 

0.02619 

0.02910 

0.03201 

0.03492 

88 

2 

0.03492 

0.03783 

0.04075 

0.04366 

0.04658 

0.04949 

0.05241 

87 

3 

0.05241 

0.05533 

0.05824 

0.06116 

0.06408 

0.06700 

0.06993 

86 

4 

0.06993 

0.07285 

0.08578 

0.07870 

0.08163 

0.08456 

0.08749 

85 

5 

0.08749 

0.09042 

0.09335 

0.09629 

0.09923 

0.10216 

0.10510 

84 

6 

0.10510 

0.10805 

0.11099 

0.11394 

0.11688 

0.11983 

0.12278 

83 

7 

0.12278 

0.12574 

0.12869 

0.13165 

0.13461 

0.13758 

0.14054 

82 

8 

0.14054 

0.14351 

0.14648 

0.14945 

0.15243 

0.15540 

0.15838 

81 

9 

0.15838 

0.16137 

0.16435 

0.16734 

0.17033 

0.17333 

0.17633 

80 

10 

0.17633 

0.17933 

0.18233 

0.18534 

0.18835 

0.19136 

0.19438 

79 

11 

0.19438 

0.19740 

0.20042 

0.20345 

0.20648 

0.20952 

0.21256 

78 

12 

0.21256 

0.21560 

0.21864 

0.22169 

0.22475 

0.22781 

0.23087 

77 

13 

0.23087 

0.23393 

0.23700 

0.24008 

0.24316 

0.24624 

0.24933 

76 

14 

0.24933 

0.25242 

0.25552 

0.25862 

0.26172 

0.26483 

0.  -26795 

75 

i 
15 

0.26795 

0.27107 

0.27419 

0.27732 

0.28046 

0.28360 

0.28675 

74 

16 

0.28675 

0.28990 

0.29305 

0.29621 

0.29938 

0.30255 

0.30573 

73 

17 

0.30573 

0.30891 

0.31210 

0.31530 

0.31850 

0.32171 

0.32492 

72 

18 

0.32492 

0.32814 

0.33136 

0.33460 

0.33783 

0.34108 

0.34433 

71 

19 

0.34433 

0.34758 

0.35085 

0.35412 

0.35740 

0.36068 

0.36397 

70 

20 

0.36397 

0.36727 

0.37057 

0.37388 

0.37720 

0.38053 

0.38386 

69 

21 

0.38386 

0.38721 

0.39055 

0.39391 

0.39727 

0.40065 

0.40403 

68 

22 

0.40403 

0.40741 

0.41081 

0.41421 

0.41763 

0.42105 

0.42447 

67 

23 

0.42447 

0.42791 

0.43136 

0.43481 

0.43828 

0.44175 

0.44523 

66 

24 

0.44523 

0.44872 

0.45222 

0.45573 

0.45924 

0.46277 

0.46631 

65 

25 

0.46631 

0.46985 

0.47341 

0.47698 

0.48055 

0.48414 

0.48773 

64 

26 

0.48773 

0.49134 

0.49495 

0.49858 

0.50222 

0.50587 

0.50953 

63 

27 

0.50953 

0.51320 

0.51688 

0.52057 

0.52427 

0.52798 

0.53171 

62 

0.53171 

0.53545 

0.53920 

0.54296 

0.54673 

0.55051 

0.55431 

61 

29 

0.55431 

0.55812 

0.56194 

0.56577 

0.56962 

0.57348 

0.57735 

60 

30 

0.57735 

0.58124 

0.58513 

0.58905 

0.59297 

0.59691 

0.60086 

59 

31 

0.60086 

0.60483 

0.60881 

0.61280 

0.61681 

0.62083 

0.62487 

58 

32 

0.62487 

0.62892 

0.63299 

0.63707 

0.64117 

0.64528 

0.64941 

57 

33 

0.64941 

0.65355 

0.65771 

0.66189 

0.66608 

0.67028 

0.67451 

56 

34 

0.67451 

0.67875 

0.68301 

0.68728 

0.69157 

0.69588 

0.70021 

55 

35 

0.70021 

0.70455 

0.70891 

0.71329 

0.71769 

0.72211 

0.72654 

54 

36 

0.72654 

0.73100 

0.73547 

0.73996 

0.74447 

0.74900 

0.75355 

53 

37 

0.75355 

0.75812 

0.76272 

0.76733 

0.77196 

0.77661 

0.78129 

52 

38 

0.78129 

0.78598 

0.79079 

0.79544 

0.80020 

0.80498 

0.80978 

51 

39 

0.80978 

0.81461 

0.81946 

0.82434 

0.82923 

0.83415 

0.83910 

50 

40 

0.83910 

0.84407 

0.84906 

0.85408 

0.85912 

0.86419 

0.86929 

49 

41 

0.86929 

0.87441 

0.87955 

0.88473 

0.88992 

0.89515 

0.90040 

48 

42 

0.90040 

0.90569 

0.91099 

0.91633 

0.92170 

0.92709 

0.93252 

47 

43 

0.93252 

0.93797 

0.94345 

0.94896 

0.95451 

0.96008 

0.96569 

46 

44 

0.96569 

0.97133 

0.97700 

0.98270 

0.98843 

0.99420 

1.00000 

45 

60' 

50' 

40 

30' 

20' 

10' 

0' 

Z 
£ 

COTANGENT. 

270         NATIONAL  TUBE  COMPANY. 

MATHEMATICAL  TABLES.  (CONTINUED.) 

I 

COTANGENT. 

I 

0' 

10' 

20' 

30' 

40' 

50' 

60' 

0 

00 

343.77371 

171.88540 

114.58865 

85.93979 

68.75009 

57.28996 

89 

1 

57.28996 

49.10388 

42.96408 

38.18846 

34.36777 

31.24158 

28.63625 

88 

2 

28.63625 

26.43160 

24.54176 

22.90377 

21.47040 

20.20555 

19.08114 

87 

3 

19.08114 

18.07498 

17.16934 

16.34986 

15.60478 

14.92442 

14.30067 

86 

4 

14.30067 

13.72674 

13.19688 

12.70621 

12.25051 

11/82617 

11.43005 

85 

5 

11.43005 

11.05943 

10.71191 

10.38540 

10.07803 

9.78817 

9.51430 

84 

6 

9.51436 

9.25530 

9.00983 

8.77689 

8.55555 

8.34496 

8.14435 

83 

7 

8.14435 

7.95302 

7.77035 

7.59575 

7.  -42871 

7.26873 

7.11537 

82 

8 

7.11537 

6.96823 

6.82694 

6.69116 

6.56055 

6.43484 

6.31375 

81 

9 

6.31375 

6.19703 

6.08444 

5.97576 

5.87080 

5.76937 

5.67128 

80 

10 

5.67128 

5.57638 

5.48451 

5.39552 

5.30928 

5.22566 

5.14455 

79 

11 

5.14455 

5.06584 

4.98940 

4.91516 

4.84300 

4.77286 

4.70463 

78 

12 

4.70463 

4.63825 

4.57363 

4.51071 

4.44942 

4.38969 

4.33148 

77 

13 

4.33148 

4.27471 

4.21933 

4.16530 

4.11256 

4.06107 

4.01078 

76 

14 

4.01078 

3.96165 

3.91364 

3.86671 

3.82083 

3.77595 

3.73205 

75 

15 

3.73205 

3.68909 

3.64705 

3.60588 

3.56557 

3.52609 

3.48741 

74 

16 

3.48741 

3.44951 

3.41236 

3.37594 

3.34023 

3.30521 

3.27085 

73 

17 

3.27085 

3.23714 

3.20406 

3.17159 

3.13972 

3.10842 

3.07768 

72 

18 

3.07768 

3.04749 

3.01783 

2.98869 

2.96004 

2.93189 

2.90421 

71 

19 

2.90421 

2.87700 

2.85023 

2.82391 

2,79802 

2  .  77254 

2.74748 

70 

20 

2.74748J  2.72281 

2.69853 

2.67462 

2.65109 

2.62791 

2.60509 

69 

21 

2.605091  2.58261 

2.56046 

2.53865 

2.51715 

2.49597 

2.47509 

68 

22 

2.47509 

2.45451 

2.43422 

2.41421 

2.39449 

2.37504 

2.35585 

67 

23 

2.35585 

2.&S693 

2.31826 

2.29984 

2.28167 

2.26374 

2.24604 

66 

24 

2.24604 

2.22857 

2.21132 

2.19430 

2.17749 

2.16090 

2.14451 

65 

25 

2.14451 

2.12a32 

2.11233 

2.09654 

2.08094 

2.06553 

2.05030 

64 

26 

2.05030 

2.03526 

2.02039 

2.00569 

.99116 

1.97680 

1.96261 

63 

27 

.96261 

1.94858 

1.93470 

1.92098 

.90741 

1.89400 

1.88073 

62 

28 

.88073 

1.86760 

.85462 

1.84177 

.82906 

1.81649 

.80405 

61 

29 

.80405 

1.79174 

.77955 

1.76749 

.75556 

1.74375 

.73205 

60 

30 

.73205 

1.72047 

.70901 

1.69766 

.68643 

1.67530 

.66428 

59 

31 

.66428 

1.65337 

.64256 

1.63185 

.62125 

1.61074 

.60033 

58 

32 

.60033 

1.59002 

.57981 

1.56969 

.55966 

1.54972 

.53987 

57 

33 

.53987 

1.53010 

.52043 

1.51084 

.50133 

1.49190 

.48256 

56 

34 

.48256 

1.47330 

.46411 

1.45501 

.44598 

1.43703 

.42815 

55 

35 

.42815 

1.41934 

.41061 

1.40195 

.39336 

1.38484 

.37638 

54 

36 

.37638 

1.36800 

.35968 

1.35142 

.34323 

1.33511 

.32704 

53 

37 

.32704 

1.31904 

.31110 

1.30323 

.29541 

1.28764 

.27994 

52 

38 

.27994 

1.27230 

.26471 

1.25717 

.24969 

1.24227 

.23490 

51 

39 

.23490 

1.22758 

.22031 

1.21310 

.20593 

1.19882 

.19175 

50 

40 

.19175 

1.18474 

.17777 

1.17085 

.16398 

1.15715 

.15037 

49 

41 

.15037 

1.14363 

.13694 

1.13029 

.12369 

1.11713 

.11061 

48 

42 

.11061 

1.10414 

.09770 

1.09131 

.08496 

1.07864 

.07237 

47 

43 

1.07237 

1.06613 

.05994 

1.05378 

.04766 

1.04158 

.03553 

46 

44 

1.03553 

1.02952 

1.02355 

1.01761 

.01170 

1.00583 

.00000 

45 

60' 

50' 

40' 

30' 

20' 

10' 

0' 

TANGENT. 

NATIONAL  TUBE  COMPANY                       271 

CIRCUMFERENCES    AND    AREAS   OF    CIRCLES. 

Diameter  from  %\  to  JOO,  advancing  chiefly  by  Eighths. 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

i 

.04909 

.00019 

2.J6 

6.6759 

3.5466 

5.  IB 

17.082 

23.221 

i 

.09818 

.00077 

3 

6.8722 

3.7583 

ix 

17  279 

23.758 

335 

.14726 

.00173 

J4 

7.0686 

3.9761 

T9S 

17.475 

24.301 

1 

.19635 

.00307 

5 

7.2649 

4.2000 

5X 

17.671 

24.850 

n 

.29452 

.00690 

% 

7.4613 

4.4301 

H 

17.868 

25.406 

i/ 

.39270 

.01227 

7 

7.6576 

4.6664 

M 

18.064 

25.967 

6^ 

.49087 

.01917 

% 

7.8540 

4.9087 

ii 

18.261 

26.535 

& 

.58905 

.02761 

9 

8.0503 

5.1572 

7X 

18.457 

27.109 

A 

.68722 

.03758 

% 

8.2467 

5.4119 

ii 

18.653 

27.688 

11 

8.4430 

5.6727 

M 

.78540 

.04909 

% 

8.6394 

5.9396 

6. 

18.&50 

28.274 

9 

.88357 

.06213 

13 

8.8357 

6.2126 

IX 

19.242 

29.465 

5 

.98175 

.07670 

% 

9.0321 

6.4918 

i/; 

19.635 

30.680 

n 

1.0799 

.09281 

ii 

9.2284 

6.7771 

% 

20.028 

31.919 

D 

1.1781 

.11045 

IX 

20.420 

33.183 

13 

1.2763 

.12962 

3. 

9.4248 

7.0686 

% 

20.813 

34.472 

7 

1.3744 

.15033 

i 

9.6211 

7.3662 

H 

21.206 

35.785 

II 

1.4726 

.17257 

x6 

9.8175 

7.6699 

21.598 

37.122 

3 

10.014 

7.9798 

7l3 

1.5708 

.19635 

J4 

10.210 

8.2958 

7. 

21.991 

38.485 

17 

1.6690 

.22166 

5 

10.407 

8.6179 

IX 

22.384 

39.871 

392 

1.7671 

.24850 

% 

10.603 

8.9462 

H 

22.776 

41.282 

19 

1.8653 

.27688 

JL 

10.799 

9.2806 

sx 

23.169 

42.718 

II 

1.9635 

.30680 

Hi 

10  996 

9.6211 

% 

23.562 

44.179 

H 

2.0617 

.33824 

9 

11.192 

9.9678 

5X 

23.955 

45.664 

H 

2.1598 

.37122 

% 

11.388 

10.321 

M 

24.347 

47.173 

11 

2.2580 

.40574 

TB 

11.585 

10.680 

% 

24.740 

48.707 

M 

11.781 

11.045 

ax 

2.3562 

.44179 

13 

11.977 

11.416 

8. 

25.133 

50.265 

§5 

2.4544 

\47937 

% 

12.174 

11.793 

25.525 

51.849 

|g 

2.5525 

.51849 

ii 

12.370 

12.177 

H 

25.918 

53.456 

2j 

2.6507 

.55914 

sx 

26.311 

55.088 

lyx 

2.7489 

.60132 

4.  i 

12.566 

12.566 

/is 

26.704 

56.745 

§1 

2.8471 

.64504 

12.763 

12.962 

% 

27.096 

58.426 

16 

2.9452 

.69029 

IX 

12.959 

13.364 

a/ 

27.489 

60.132 

Si 

3.0434 

.73708 

& 

13.155 

13.772 

% 

27.882 

61.862 

J4 

13.352 

14.186 

1.  t 

3.1416 

.7854 

T*8 

13.548 

14.607 

9. 

28.274 

63.617 

3.3379 

.8866 

3X 

13.744 

15.033 

IX 

28.667 

65.397 

|x 

3.5343 

.9940 

T?B 

13.941 

15.466 

x4 

29.060 

67.201 

A 

3.7306 

.1075 

1^ 

14.137 

15.904 

3X 

29.452 

69.029 

s 

3.9270 

.2272 

J» 

14.334 

16.349 

IX 

29.845 

70.882 

i 

4.1233 

.3530 

% 

14.530 

16.800 

% 

30.238 

72.760 

4.3197 

.4849 

11 

14.726 

17.257 

7* 

30.631 

74.662 

/e 

4.5160 

.6230 

M 

14.923 

17.728 

31.023 

76.589 

IX 

4.7124 

.7671 

13 

15.119 

18.190 

9 

4.9087 

.9175 

7X 

15.315 

18.665 

10. 

31.416 

78.540 

% 

5.1051 

2.0739 

if 

15.512 

19.147 

31.809 

80.516 

11 

5.3014 

2.2365 

IX 

32.201 

82.516 

M 

5.4978 

2.4053 

5. 

15.708 

19.635 

/i 

32.594 

84.541 

13 

5.6941 

2.5802 

TB 

15.904 

20.129 

v^ 

32.987 

86.590 

% 

5  8905 

2.7612 

y 

16.101 

20.629 

% 

33.379 

88.664 

18 

6.0868 

2.9483 

T^ 

16.297 

21.135 

% 

as.  772 

90.763 

I/ 

16.493 

21.648 

% 

34.165 

92.886 

2. 

6.2832 

3.1416 

^ 

16.690 

22.166 

A 

6.4795 

3  3410 

% 

16.886 

22.691 

11. 

34.558 

95.033 

flr.                                                  J 

272                      NATIONAL  TUBE  COMPANY. 

CIRCUMFERENCES   AND    AREAS    OF    CIRCLES. 

(CONTINUED.) 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

11-/6 

34.950 

97.205 

17.% 

54.585 

237.10 

23.% 

74.220 

438.36 

35.343 

99.402 

54.978 

240.53 

74.613 

443.01 

3X 

35.736 

101.62 

% 

55.371 

243.98 

% 

75.006 

447.69 

x^ 

36.128 

103.87 

M 

55.763 

247.45 

% 

36.521 

106.14 

% 

56.156 

250.95 

24. 

75.398 

452.39 

%. 

36.914 

108.43 

75.791 

457.11 

% 

37.306 

110.75 

18. 

56.549 

254.47 

/4 

76.184 

461.86 

J| 

56.941 

258.02 

az 

76.576 

466.64 

12. 

37.699 

113.10 

57.334 

261.59 

/^ 

76.969 

471.44 

38.092 

115.47 

3X 

57.727 

265.18 

KX 

77.362 

476.26 

IX 

38.485 

117.86 

L£i 

58.119 

268.80 

3X 

77.754 

481.11 

% 

38.877 

120.28 

% 

58.512 

272.45 

% 

78.147 

485.98 

fij 

39.270 

122.72 

a/ 

58.905 

276.12 

% 

39.663 

125.19 

% 

59.298 

279.81 

25. 

78.540 

490.87 

ax 

40.055 

127.68 

78.933 

495.79 

% 

40.448 

130.19 

19. 

59.690 

283.53 

IX 

79.325 

500.74 

60.083 

287.27 

% 

79.718 

505.71 

13. 

40.841 

132.73 

ix; 

60.476 

291.04 

IX 

80.111 

510.71 

41.233 

135.30 

% 

60.8(58 

294.83 

% 

80.503 

515.72 

IX 

41.626 

137.89 

IX, 

61.261 

298.05 

3X 

80.89(5 

520.77 

%  • 

42.019 

140.50 

% 

61.654 

302.49 

% 

81.289 

525.84 

1Z 

42.412 

143.14 

% 

62.046 

306.35 

KX 

42.804 

145.80 

% 

62.439 

310.24 

26. 

81.681 

530.93 

% 

43.197 

148.49 

82.074 

536.05 

% 

43.590 

151.20 

20. 

62.832 

314.16 

IX 

82.467 

541.19 

M 

63.225 

318.10 

% 

82.860 

546.35 

14. 

43.982 

153.94 

63.617 

322.06 

i£ 

83.252 

551.55 

44.375 

156.70 

% 

64  010 

3-26.05 

% 

83.645 

556.76 

M 

44.768 

159.48 

v& 

64.403 

330.06 

% 

84.038 

562.00 

32 

45.160 

162.30 

% 

(54.795 

334.10 

% 

84.430 

567.27 

xii 

45.553 

165.13 

H 

65.188 

338.16 

5/ 

45.946 

167.99 

H 

65.581 

342.25 

27. 

84.823 

572.56 

§i 

46.338 

170.87 

ix 

85.216 

577.87 

% 

46.731 

173.78 

21. 

65.973 

346.36 

H 

85.608 

583.21 

/^c 

c,ii.:i(ii; 

350.50 

a2 

8(5.001 

588.57 

15. 

47.124 

176.71 

M 

66.759 

&54.66 

VX, 

86.394 

593.96 

^ 

47.517 

179.67 

% 

67.152 

358.84 

% 

86.786 

599.37 

47.909 

182.65 

L£ 

67.544 

363.05 

3X 

87.179 

604.81 

32 

48.302 

185.66 

% 

67.937 

3(57.28 

7X 

87.572 

610.27 

/^ 

48.695 

188.69 

M 

68.330 

371.54 

% 

49.087 

191.75 

% 

68.722 

375.83 

28. 

87.965 

615.75 

% 

49.480 

194.83 

x4 

88.357 

621.26 

% 

49.873 

197.93 

22. 

69.115 

380.13 

/x; 

88.750 

626  80 

ix 

69.508 

384.46 

% 

89.143 

632.36 

16. 

50.265 

201.06 

IX 

69.900 

388.82 

IX 

89.535 

637.94 

50.658 

204.22 

% 

70.293 

393.20 

% 

H«.).«>28 

643.55 

IX 

51.051 

207.39 

ix. 

70.686 

397.61 

ax. 

90.321 

649.18 

% 

51.444 

210.60 

% 

71.079 

402.04 

% 

90.713 

654.84 

l£ 

51.836 

213.82 

ax. 

71.471 

406.49 

B/j 

52.229 

217.08 

% 

71.864 

410.97 

29. 

91.106 

660.52 

9i 

52.622 

220.35 

$ 

91  .499 

666.23 

7^ 

53.014 

223.65 

23. 

72.257 

415.48 

91.892 

671.96 

$ 

72.649 

420.00 

sz 

92.284 

677.71 

17. 

53.407 

226.98 

73.042 

424.56 

/^ 

92.C.77 

683.49 

53.800 

230.33 

% 

73.435 

429.13 

% 

93.070 

689.30       i 

M 

54.192 

233.71 

/^ 

73.827 

433.74 

H 

93.462 

695.13 

NATIONAL  TUBE  COMPANY.                      273 

CIRCUMFERENCES    AND    AREAS    OF    CIRCLES. 

(CONTINUED.) 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

29.% 

93.855 

700.98 

36.^ 

113.490 

1025.0 

42.% 

133.125 

1410.3 

113.883 

1032.1 

133.518 

1418.6 

30. 

94.248 

706.86 

a2 

114.275 

1039.2 

&£ 

133.910 

1427.0 

94.640 

712.76 

/^ 

114.668 

1046.3 

M 

134.303 

1435.4 

/4 

95.033 

718.69 

5X 

115.061 

1053.5 

TX 

134.696 

1443.8 

% 

95.426 

724.64 

M 

115.454 

1060.7 

12 

95.819 

730.62 

% 

115.846 

1068.0 

43. 

135.088 

1452.2 

% 

96.211 

736.62 

/4 

135.481 

1460.7 

% 

96.604 

742.64 

37. 

116.239 

1075.2 

/4 

135.874 

1469.1 

% 

96.997 

748.69 

K 

116.633 

1082.5 

% 

136.267 

1477.6 

117.024 

1089.8 

i^ 

136.659 

1486  2 

31. 

97.389 

754.77 

% 

117.417 

1097.1 

R^ 

137.052 

1494.7 

H 

97.782 

760.S7 

/^ 

117,810 

1104,5 

M 

137.445 

1503.3 

98.175 

766.99 

% 

118.202 

1111.8 

% 

137.837 

1511.9 

% 

98.567 

773.14 

a/ 

118.596 

1119.2 

te 

98.960 

779.31 

% 

118.988 

1126.7 

44. 

138.230 

1520.5 

% 

99.353 

785.51 

^x 

138.623 

1529.2 

99.746 

791.73 

38. 

119.381 

1134.1 

H 

139.015 

1537.9 

% 

100.138 

797.98 

/^c 

119.773 

1141.6 

s2 

139.408 

1546.6 

H 

120.166 

1149.1 

& 

139.801 

1555.3 

32. 

100.531 

804.25 

a2 

120.559 

1156.6 

i2 

140.194 

1564.0 

If 

100.924 

810.54 

Jij 

120.951 

1164.2 

% 

140.586 

1572.8 

M 

101.316 

816.86 

% 

121.344 

1171.7 

% 

140.979 

1581  6 

?B 

101.709 

823.21 

% 

121.737 

1179.3 

^ 

102.102 

829.58 

% 

122.129 

1186.9 

45. 

141.372 

1590.4 

% 

102.494 

835.97 

ix 

141.764 

1599.3 

M 

102.887 

842.39 

39. 

122.522 

1194.6 

H 

142.157 

1608.2 

% 

103.280 

848.83 

ix 

122.915 

1202.3 

3X 

142.550 

1617.0 

24 

128.808 

1210.0 

^ 

142.942 

1626.0 

33. 

103.673 

855.30 

sx 

123.700 

1217.7 

% 

143.335 

1634.9 

104.065 

861.79 

i^ 

124.093 

1225.4 

M 

143.728 

1643.9 

^4 

104.458 

868.31 

% 

124.486 

1233.2 

7X 

144.121 

1652.9 

% 

104.  851 

874.85 

M 

124.878 

1241.0 

J^> 

105.243 

881.41 

7X 

125.271 

1248.8 

46. 

144.513 

1661.9 

% 

105.1536 

888.00 

i^ 

144.906 

1670.9 

M 

106.029 

894.62 

40. 

125.664 

1256.6 

J4 

145.299 

1680.0 

72 

106.421 

901.26 

126.056 

1264.5 

% 

145.691 

1689.1 

H 

126.449 

1272.4 

i^ 

146.084 

1398.2 

34. 

106.814 

907.92 

a? 

126.842 

1280.3 

7& 

146.477 

1707.4 

107.207 

914.61 

/^ 

127.235 

1288.2 

M 

146.869 

1716.5 

M 

107.600 

921.32 

&X 

127.627 

1296.2 

7X 

147.262 

1725.7 

% 

107.992 

928.06 

3£ 

128.020 

1304.2 

^ 

108.385 

934.82 

% 

128.413 

1312.2 

47. 

147.655 

1734.9 

% 

108.778 

941.61 

148.048 

1744.2 

9£ 

109.170 

948.42 

41. 

128.805 

1320.3 

H 

148.440 

1753.5 

% 

109.563 

955.25 

ix 

129.198 

1328.3 

&z 

148.833 

1762.7 

H 

129.591 

1336.4 

\fa 

149.226 

1772.1 

35. 

109.956 

962.11 

32 

129.983 

1344.5 

% 

149.618 

1781.4 

H 

110.348 

969.00 

^ 

130.376 

1352.7 

M 

150.011 

1790.8 

/4 

110.741 

975.91 

% 

130.769 

1360.8 

% 

150.404 

1800.1 

% 

111.134 

982.84 

M 

131.161 

1369.0 

% 

111.527 

989.80 

8 

131.554 

1377.2 

48. 

150.796 

1809.6 

% 

111.919 

996.78 

IX 

151.189 

1819.0 

K 

112.312 

1003.8 

42. 

131.947 

1385.4 

J4 

151.582 

1828.5 

% 

112.705 

1010.8 

ix 

182.340 

1393.7 

3X 

151.975 

1887.9 

36. 

113.097 

1017.9 

1     J4 

132.732 

1402.0 

^ 

152.367 

1847.5 

874                       NATIONAL  TUBE  COMPANY. 

CIRCUMFERENCES    AND    AREAS    OF    CIRCLES. 

(CONTINUED.) 

Diam. 

Circum. 

Area. 

Diam 

Circum. 

Area. 

Diam 

Circum. 

Area. 

48.% 

152.760 

1857.0 

54.% 

172.395 

2365.0 

61. 

191.637 

2922.5 

K 

153.153 

1866.5 

ix 

192.030 

2934.5 

ys 

153.545 

1876.1 

55. 

172.788 

2375.8 

M 

192.423 

2946.5 

H 

173.180 

2386.6 

RZ 

192.815 

2958.5 

49. 

153.938 

1885.7 

M 

173.573 

2397.5 

~L£ 

193.208 

2970.6 

% 

154.331 

1895.4 

% 

173.966 

2408.3 

% 

193.601 

2982.7 

M 

154.723 

1905.0 

/^ 

174.358 

2419.2 

% 

193.993 

2994.8 

% 

155.116 

1914.7 

% 

174.751 

2430.1 

% 

194.386 

3006.9 

UL 

155.509 

1924.4 

% 

175.144 

2441.1 

% 

155.902 

1934.2 

% 

175.536 

2452.0 

62. 

194.779 

3019.1 

3X 

156.294 

1943.9 

195.171 

3031.3 

% 

156.687 

1953.7 

56. 

175.929 

2463.0 

M 

195.564 

3043.5 

12 

176.322 

2474.0 

% 

195.957 

3055.7 

50. 

157.080 

1963.5 

M 

176.715 

2485.0 

H 

196.350 

3068.0 

K 

157.472 

1973.3 

% 

177.107 

2496.1 

% 

196.742 

3080.3 

157.865 

1983.2 

LX 

177.500 

2507.2 

ax 

197.135 

3092.6 

H 

158.258 

1993.1 

% 

177.893 

2518.3 

% 

197.528 

3104.9 

Lg 

158.650 

2003.0 

% 

178.285 

2529.4 

% 

159.043 

2012.9 

?/8 

178.678 

2540.6 

63. 

197.920 

3117.2 

M 

159.436 

2022.8 

te 

198.313 

3129.6 

% 

159.829 

2032.8 

57. 

179.071 

2551.8 

198.706 

3142.0 

12 

179.463 

2563.0 

s2 

199.098 

3154.5 

51. 

160.221 

2042.8 

IX 

179.856 

2574.2 

j/> 

199.491 

3166.9 

x^ 

160.614 

2052.8 

% 

180.249 

2585.4 

% 

199.884 

3179.4 

/4 

161.007 

2062.9 

L^J 

180.642 

2596.7 

ax 

200.277 

3191.9 

32 

161.399 

2073.0 

SX 

181.034 

2608.0 

% 

200.669 

3204.4 

i£ 

161.792 

2083.1 

% 

181.427 

2619.4 

8 

162.185 

2093.2 

% 

181.820 

2630.7 

64. 

201.062 

3217.0 

H 

162.577 

2103.3 

H 

201.455 

3229.6 

% 

162.970 

2113.5 

58. 

182.212 

2642.1 

IX 

201.847 

3242.2 

K 

182.605 

2653.5 

% 

202.240 

3254.8 

52. 

163.363 

2123.7 

182.998 

2664.9 

v& 

202.633 

3267.5 

^6 

168.75(5 

2133.9 

32 

183.390 

2676.4 

% 

203.025 

3280.1 

H 

164.148 

2144.2 

/^ 

183.783 

2687.8 

ax_ 

203.418 

3292.8 

82 

164.541 

2154.5 

% 

184.176 

2699.3 

% 

203.811 

3305.6 

^5 

164.934 

2164.8 

% 

184.569 

2710.9 

% 

165.326 

2175.1 

% 

184.961 

2722.4 

65. 

204.204 

3318.3 

94 

165.719 

2185.4 

H 

204.596 

3331.1 

% 

166.112 

2195.8 

59. 

185.354 

2734.0 

204.989 

3343.9 

185.747 

2745.6 

a| 

205.382 

3356.7 

53. 

166.504 

2206.2 

/4 

186.139 

2757.2 

LX 

205.774 

3369.6 

M 

166.897 

2216.6 

% 

186.532 

2768.8 

% 

206.167 

3382.4 

167.290 

2227.0 

T£ 

186.925 

2780.5 

ax 

206.560 

3395.3 

32 

167.683 

2237.5 

% 

187.317 

2792.2 

72 

206  952 

3408.2 

/^ 

168.075 

2248.0 

3X 

187.710 

2803.9 

% 

168.468 

2258.5 

% 

188.103 

2815.7 

66. 

207.345 

3421.2 

a/ 

168.861 

2269.1 

12 

207.738 

3434.2 

/•I 

169.253 

2279.6 

60. 

188.496 

2827.4 

H 

208.131 

3447.2 

M 

188.  S88 

2839.2 

32 

208.523 

3460.2 

54. 

169.646 

2290.2 

189.281 

2851.0 

12 

208.916 

3473.2 

170.039 

2300.8 

2s 

189.674 

2862.9 

% 

209.309 

3486.3 

/4 

170.431 

2311.5 

1^5 

190.066 

2874.8 

ax 

209.701 

3499.4 

a2 

170.824 

2322.1 

7& 

190.459 

2886.6 

% 

210.094 

3512.5 

£» 

171  217 

2332.8 

% 

190.852 

2898.6 

B 

171.609 

2343.5 

7% 

191.244 

2910.5 

67. 

210.487 

3525.7 

*M 

172.002 

2354.3 

H 

210.879 

3538.8 

|H=                                                                                           ^ 

NATIONAL  TUBE  COMPANY.                      275 

CIRCUMFERENCES    AND    AREAS  OF   CIRCLES. 

(CONTINUED.) 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

67.  U 

211.272 

3552.0 

73.^ 

230.907 

4242.9 

79.  g 

250.542 

4995.2 

211.665 

3565.2 

231.300 

4257.4 

250.935 

5010.9 

if 

212.058 

3578.5 

M 

231.692 

4271.8 

% 

212.450 

3591.7 

H 

232.085 

4286.3 

80. 

251.327 

5026.5 

az 

212.843 

3605.0 

i/i 

251.720 

5042.3 

7Z 

213.236 

3618.3 

74. 

232.478 

4300.8 

•y. 

252.113 

5058.0 

^ 

232.871 

4315.4 

% 

252.506 

5073.8 

1     68. 

213.628 

3631.7 

233.263 

4329.9 

& 

252.898 

5089.6 

214.021 

3645.0 

9s 

233.656 

4344.5 

7S 

253.291 

5105.4 

iz 

214.414 

3658.4 

\&> 

234.049 

4359.2 

M 

253.684 

5121.2 

% 

214.806 

3671.8 

% 

234.441 

4373.8 

% 

254.076 

5137.1 

iz 

215.199 

8685.3 

az 

234.834 

4388.5 

% 

215.592 

3698.7 

H 

235.227 

4403.1 

81. 

254.469 

5153.0 

a/ 

215.984 

3712.2 

iz 

254.862 

5168.9 

n 

216.377 

3725.7 

75. 

235.619 

4417.9 

H 

255.254 

5184.9 

M 

236.012 

4432.6 

sz 

255.647 

5200.8 

\     69. 

216.770 

3739.3 

236.405 

4447.4 

/^ 

256.040 

5216.8 

217.163 

3752.8 

8Z 

236.798 

4462.2 

% 

256.433 

5232.8 

H 

217.555 

3766.4 

% 

237.190 

4477.0 

M 

256.825 

5248.9 

sz 

217.948 

3780.0 

% 

237.583 

4491.8 

% 

257.218 

5264.9 

iz 

218.341 

3793.7 

3Z 

237.976 

4506.7 

% 

218.733 

3807.3 

% 

238.368 

4521.5 

82. 

257.611 

5281.0 

az 

219.126 

3821.0 

258.003 

5297.1 

% 

219.519 

3834.7 

76. 

238.761 

4536.5 

M. 

258.396 

5313.3 

iz. 

239.154 

4551.4 

% 

258.789 

5329.4 

70. 

219.911 

3848.5 

H 

239.546 

4566.4 

L£ 

259.181 

5345.6 

220.304 

3862  2 

az 

239.939 

4581.3 

% 

259.574 

5361.8 

/4 

220.697 

3876.0 

/^ 

240.332 

4596.3 

% 

259.967 

5378.1 

sz 

221.090 

3889.8 

BX 

240.725 

4611.4 

% 

260.359 

5394  3 

ijj 

221.482 

3903.6 

M 

241.117 

4626.4 

% 

221.875 

3917.5 

% 

241.510 

4641.5 

83. 

260.752 

5410.6 

a 

222.268 

3931.4 

261.145 

5426.9 

7Z 

222.660 

3945.3 

77. 

241.903 

4656.6 

M 

261.538 

5443.3 

if? 

242.295 

4671.8 

RZ 

261.930 

5459.6 

71. 

223.053 

3959.2 

H 

242.688 

4686.9 

ty> 

262.323 

5476.0 

ix 

223.446 

3973.1 

3X 

243.081 

4702.1 

KZ 

262.716 

5492.4 

H 

223.838 

3987.1 

\fa 

243.473 

4717.3 

ax 

263.108 

5508.8 

% 

224.231 

4001.1 

% 

243.866 

4732.5 

% 

263.501 

5525.3 

i2 

224.624 

4015.2 

% 

244.259 

4747.8 

1% 

225.017 

4029.2 

% 

244.652 

4763.1 

84. 

263.894 

5541.8 

H 

225.409 

4043.3 

264.286 

5558.3 

% 

225.802 

4057.4 

78. 

245.044 

4778.4 

IX 

264.679 

5574.8 

^ 

245.437 

4793.7 

9s 

265.072 

5591.4 

72. 

226.195 

4071.5 

245.  830 

4809.0 

1Z 

265.465 

5607.9 

K 

226.587 

4085.7 

% 

246.222 

4824.4 

% 

265.857 

5624.5 

J4 

226.980 

4099.8 

^a 

246.615 

4839.8 

3X 

266.250 

5641.2 

&z 

227.373 

4114.0 

% 

247.008 

4855.2 

7Z 

266.643 

5657.8 

1^ 

227.765 

4128.2 

M 

247.400 

4870.7 

?8 

228.158 

4142.5 

% 

247.793 

4886.2 

85. 

267.035 

5674.5 

M 

228.551 

4156.8 

267.428 

5691.2 

% 

228.944 

4171.1 

79. 

248.186 

4901.7 

\A 

267.821 

5707.9 

ix 

248.579 

4917.2 

az 

268.213 

5724.7 

73. 

229.336 

4185.4 

u 

248.971 

4932.7 

7& 

268.606 

5741.5 

14 

229.729 

4199.7 

a2 

249.364 

4948.3 

5Z 

268.999 

5758.3 

/4 

230.122 

4214.1 

i2 

249.757 

4963.9 

az 

269.392 

5775.1 

% 

230.514 

4228.5 

% 

250.149 

4979.5 

% 

269.784 

5791.9 

i,  JJ 

276                      NATIONAL  TUBE  COMPANY. 

CIRCUMFERENCES    AND    AREAS    OF   CIRCLES. 

(CONTINUED.) 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

86. 

270.177 

5808.8 

90.% 

285.492 

6486.0 

95.% 

300.415 

7181.8 

270.570 

5825.7 

3 

300.807 

7200.6 

IA 

270.962 

5842.6 

91. 

285.885 

6503.9 

% 

301.200 

7219.4 

% 

271.355 

5859.6 

y& 

286.278 

6521.8 

L£ 

271.748 

5876.5 

14 

286.670 

6539.7 

96. 

301.593 

7238.2 

% 

272.140 

5893.5 

s3 

287.063 

6557.6 

i/ 

301.986 

7257.1 

% 

272.533 

5910.6 

Vz 

287.456 

6575.5 

M 

302.378 

7276.0 

72 

272.926 

5927.6 

PB 

287.848 

6593.5 

% 

302.771 

7294.9 

' 

M 

288.241 

6611.5 

V% 

303,164 

7313.8 

87. 

273.319 

5944.7 

% 

288.634 

6629.6 

% 

303.556 

7332.8 

273.711 

5961.8 

'itA 

303.949 

7351.8 

H 

274.104 

5978.9 

92. 

289.027 

6647.6 

% 

304.342 

7370.8 

az 

274.49? 

5996.0 

/*£ 

289.419 

6665.7 

LZ 

274.889 

6013.2 

M 

283.812 

6683.8 

97. 

304.734 

7389.8 

N 

275.282 

6030.4 

% 

290.205 

6701.9 

M 

305.127 

7408.9 

3/: 

275.675 

6047.6 

^ 

290.597 

6720.1 

305.520 

7428.0 

% 

276.067 

6064.9 

% 

290.990 

6738.2 

% 

305.913 

7447.1 

M 

291.383 

6756.4 

\& 

306.305 

7466.2 

88. 

276.460 

6082.1 

% 

291.775 

6774.7 

7& 

306.698 

7485.3 

276  853 

6099.4 

H 

307.091 

7504.5 

ix 

277.246 

6116.7 

93. 

292.168 

6792.9 

% 

307.483 

7523.7 

a2 

277.638 

6134.1 

YB 

292.561 

6811.2 

/^ 

278.031 

6151.4 

292.964 

6829.5 

98. 

307.876 

7543.0 

% 

278.424 

6168.8 

% 

293.346 

6847.8 

i/ 

308.269 

7562.2 

a/ 

278.816 

6186.2 

L& 

293.739 

6866.1 

M 

308.661 

7581.5 

7-i 

279.209 

6203.7 

% 

291.132 

6884.5 

% 

309.054 

7600.8 

' 

M 

294.524 

6902.9 

L^ 

309.447 

7620.1 

89. 

279.602 

6221.1 

% 

294.917 

6921  3 

% 

309.840 

7639.5 

279.994 

6238.6 

% 

310.232 

7658.9 

24 

280.387 

6256.1 

94. 

295.310 

6939.8 

% 

310.625 

7678.3 

280.780 

6273.7 

295.702 

6958.2 

2 

281.173 

6291.2 

J4 

296.095 

6976.7 

99. 

311.018 

7697.7 

KX 

281.565 

6308.8 

% 

296.488 

6995.3 

i^ 

311.410 

7717.1 

% 

281.958 

6326  4 

y% 

296.881 

7013.8 

H 

311.803 

7736.6 

% 

282.351 

6344.1 

% 

297.273 

7032.4 

% 

312.196 

7756.1 

a/ 

297.666 

7051.0 

L/j 

312.588 

7775.6 

90. 

282.743 

6361.7 

% 

298.059 

7069.6 

% 

312.981 

7795.2 

W 

283.136 

6379.4 

a/ 

313.374 

7814.8 

283.529 

6397.1 

95. 

298.451 

7088.2 

% 

313.767 

7834.4 

32 

283.921 

6414.9 

y» 

298.844 

7106.9 

IX 

284.814 

6432.6 

299.237 

7125.6 

100. 

314.159 

7854.0 

% 

284.707 

6450.4 

a| 

299.629 

7144.3 

H 

285.100 

6468.2 

g 

300.022 

7163.0 

tp  -, 

NATIONAL  TUBE  COMPANY.         277 

FIFTH  ROOTS  AND  FIFTH  POWERS. 

Power. 

No.  or 
Root. 

Power. 

No.  or 
Root. 

Power. 

No.  or 
Root. 

.0000100 

.1 

.000796 

.240 

.034503 

.51 

.0000110 

.102 

.000883 

.245 

.038020 

.52 

.0000122 

.104 

.000977 

.250 

.041820 

.53 

.0000134 

.106 

.001078 

.255 

.045917 

.54 

.0000147 

.108 

.001188 

.260 

.050328 

.55 

.0000161 

.110 

.001307 

.265 

.055073 

.56 

.0000176 

.112 

.001435 

.270 

.060169 

.57 

.0000193 

.114 

.001573 

.275 

.065636 

.58 

.0000210 

.116 

.001721 

.280 

.071492 

.59 

0000229 

.118 

.001880 

.285 

.077760 

.60 

.0000249 

.120 

.002051 

.290 

.084460 

.61 

.0000270 

.122 

.002234 

.295 

.091613 

.62 

.0000293 

.124 

.002430 

.300 

.099244 

.63 

.0000318 

.126 

.002639 

.305 

.107374 

.64 

.0000344 

.128 

.002863 

.310 

.116029 

.65 

.0000371 

.130 

.003101 

.315 

.125233 

.66 

.0000401 

.132 

.003355 

.320 

.135012 

.67 

.0000432 

.134 

.003626 

.325 

.145393 

.68 

.0000465 

.136 

.003914 

.330 

.156403 

.69 

.0000500 

.138 

.004219 

.335 

.168070 

.70 

.0000538 

.140 

.004544 

.340 

.180423 

.71 

.0000577 

.142 

.004888 

.345 

.193492 

.72 

.0000619 

.144 

.005252 

.350 

.207307 

.73 

.0000663 

.146 

.005638 

.355 

.221901 

.74 

.0000710 

.148 

.006047 

.360 

.237305 

.75 

.0000754 

.150 

.006478 

.365 

.253553 

.76 

.0000895 

.155 

.006934 

.370 

.270678 

.77 

.000105 

.160 

.007416 

.375 

.288717 

.78 

.000122 

.165 

.007924 

.380 

.307706 

.79 

.000142 

.170 

.008459 

.385 

.327680 

.80 

.000164 

.175 

.009022 

.390 

.348678 

.81 

.000189 

.180 

.009616 

.395 

.370740 

.82 

.000217 

.185 

.010240 

.400 

.393904 

.83 

.000248 

.190 

.011586 

.41 

.418212 

.84 

.000282 

•195 

.013069 

.42 

.443705 

.85 

.000320 

.200 

.014701 

.43 

.470427 

.86 

.000362 

.205 

.016492 

.44 

.498421 

.87 

.000408 

.210 

.018453 

.45 

.527732 

.88 

.000459 

.215 

.020596 

.46 

.558406 

.89 

.000515 

.220 

.022935 

.47 

.590490 

.90 

.000577 

.225 

.025480 

.48 

.624032 

.91 

.000544 

.230 

.028248 

.49 

.659082 

.92 

.000717 

.235 

.031250 

.50 

.695688 

.93 

T                                        r 

278                      NATIONAL  TUBE  COMPANY. 

Fifth  Roots  and  Fifth  Powers.    (CONTINUED.) 

Power. 

No.  or 
Root. 

Power. 

No.  or 
Root. 

Power. 

No.  or 
Root. 

.733904 

.94 

15.9495 

1.74 

525.219 

3.50 

.773781 

.95 

16.8874 

1.76 

563.822 

3.55 

.815373 

.96 

17.8690 

1.78 

604.662 

3.60 

.858734 

.97 

18.8957 

1.80 

647.835 

3.65 

.903921 

.98 

19.9690 

1.82 

693.440 

3.70 

.950990 

.99 

21.0906 

1.84 

741.577 

3.75 

1. 

1. 

22.2620 

1.86 

792.352 

3.80 

1.10408 

1.02 

23.4849 

1.88 

845.870 

3.85 

1.21665 

1.04 

24.7610 

1.90 

902.242 

3.90 

1.33823 

1.06 

26.0919 

1.92 

961.58 

3.95 

1.46933 

.08 

27.4795 

1.94 

1024.00 

4.00 

1.61051 

.10 

28.9255 

1.96 

1089.62 

4.05 

1.76234 

.12 

30.4317 

1.98 

1158.56 

4.10 

1.92541 

.14 

32.0000 

2.00 

1230.95 

4.15 

2.10034 

.16 

36.2051 

2.05 

1306.91 

4.20 

2.28775 

.18 

40.8410 

2.10 

1386.58 

4.25 

2.48832 

1.20 

45.9401 

2.15 

1470.08 

4.30 

2.70271 

1.22 

51.5363 

2.20 

1557.57 

4.35 

2.93163 

1.24 

57.6650 

2.25 

1649.16 

4.40 

3.17580 

1.26 

64.3634 

2.30 

1745.02 

4.45 

3.43597 

1.28 

71.6703 

2.35 

1845.28 

4.50 

3.71293 

1.30 

79.6262 

2.40 

1950.10 

4.55 

4.00746 

1.32 

88.2735 

2.45 

2059.63 

4.60 

4.32040 

1.34 

97.6562 

2.50 

2174.03 

4.65 

4.65259 

1.36 

107.820 

2.55 

2293.45 

4.70 

5.00490 

1.38 

118.814 

2.60 

2418.07 

4.75 

5.37824 

1.40 

130.686 

2.65 

2548.04 

4.80 

5.77353 

1.42 

143.489 

2.70 

2683.54 

4.85 

6.19174 

1.44 

157.276 

2.75 

2824.75 

4.90 

6.63383 

1.46 

172.104 

2.80 

2971.84 

4.95 

7.10082 

1.48 

188.029 

2.85 

3125.00 

5.00 

7.59375 

1.50 

205.111 

2.90 

3450.25 

5.10 

8.11368 

1.52 

223.414 

2.95 

3802.04 

5.20 

8.66171 

1.54 

243.000 

3.00 

4181.95 

5.30 

9.23896 

1.56 

263.936 

3.05 

4591.65 

5.40 

9.84658 

1.58 

286.292 

3.10 

5032.84 

5.50 

10.4858 

1.60 

310.136 

3.15 

5507.32 

5.60 

11.1577 

1.62 

335.544 

3.20 

6016.92 

5.70 

11.8637 

1.64 

362.591 

3.25 

6563.57 

5.80 

12.6049 

1.66 

391.354 

3.30 

7149.24 

5.90 

13.3828 

1.68 

421.419 

3.35 

7776.00 

6.00 

14.1986 

1.70 

454.354 

3.40 

8445.96 

6.10 

15.0537 

1.72 

488.760 

3.45 

9161.33 

6.20 

NATIONAL  TUBE  COMPANY.         279 

Fifth  Roots  and  Fifth  Powers.  (CONTINUED.) 

Power. 

No.  or 
Root. 

Power. 

No.  or 
Root. 

Power. 

No.  or 
Root. 

9924.37 

6.30 

176234. 

11.2 

3043168. 

19.8 

10737. 

6.40 

192541  . 

11.4 

3200000. 

20.0 

11603. 

6.50 

210034. 

11.6 

3363232. 

20.2 

12523. 

6.60 

228776. 

11.8 

3533059. 

20.4 

13501  . 

6.70 

248832. 

12.0 

3709677. 

20.6 

14539. 

6.80 

270271  . 

12.2 

3893289. 

20.8 

15640. 

6.90 

293163. 

12.4 

4084101. 

21.0 

16807. 

7.00 

317580. 

12.6 

4282322. 

21.2 

18042. 

7.10 

343597. 

12.8 

4488166. 

21.4 

19349. 

7.20 

371293. 

13.0 

4701850. 

21.6 

20731  . 

7.30 

400746. 

13.2 

4923597. 

21.8 

22190. 

7.40 

432040. 

13.4 

5153632. 

22.0 

23730. 

7.50 

465259. 

13.6 

5392186. 

22.2 

25355. 

7.60 

500490. 

13.8 

5639493. 

22.4 

27068. 

7.70 

537824. 

14.0 

5895793. 

22.6 

28872. 

7.80 

577353. 

14.2 

6161327. 

22.8 

30771. 

7.90 

619174. 

14  .X4 

6436343. 

23.0 

32768. 

8.00 

663383. 

14.6 

6721093. 

23.2 

34868. 

8.10 

710082. 

14.8 

7015834. 

23.4 

37074. 

8.20 

759375. 

15.0 

7320825. 

23.6 

39390. 

8.30 

811368. 

15.2 

7636332. 

23.8 

41821. 

8.40 

866171. 

15.4 

7962624. 

24.0 

44371  . 

8.50 

923896. 

15.6 

8299976. 

24.2 

47043. 

8.60 

984658. 

15.8 

8648666. 

24.4 

49842. 

8.70 

1048576. 

16.0 

9008978. 

24.6 

52773. 

8.80 

1115771. 

16.2 

9381200. 

24.8 

55841  . 

8.90 

1186367. 

16.4 

9765625. 

25.0 

59049. 

9.00 

1260493. 

16.6 

10162550. 

25.2 

62403. 

9.10 

1338278. 

16.8 

10572278. 

25.4 

65908. 

9.20 

1419857. 

17.0 

10995116. 

25.6 

69569. 

9.30 

1505366. 

17.2 

11431377. 

25.8 

73390. 

9.40 

1594947. 

17.4 

11881376. 

26/0 

77378. 

9.50 

1688743. 

17.6 

12345437. 

26.2 

81537. 

9.60 

1786899. 

17.8 

12823886. 

26.4 

85873. 

9.70 

1889568. 

18.0 

13317055. 

26.6 

90392. 

9.80 

1996903. 

18.2 

13825281  . 

26.8 

95099. 

9.90 

2109061. 

18.4 

14348907. 

27.0 

100000. 

10.0 

2226203. 

18.6 

14888280. 

27.2 

110408. 

10.2 

2348493. 

18.8 

15443752. 

27.4 

121665. 

10.4 

2476099. 

19.0 

16015681  . 

27.6 

133823. 

10.6 

2609193. 

19.2 

16604430. 

27.8 

146933. 

10.8 

2747949. 

19.4 

17210368. 

28.0 

161051. 

11.0 

2892547. 

19.6 

17833868. 

28.2 

280 

NATIONAL  TUBE  COMPANY. 

Fifth 

Roots 

and  Fifth  Powers. 

(CONTINUED.) 

Power. 

No.  or 
Root. 

Power. 

No.  or 
Root. 

^wer.    N0oo0r 

18475309. 
19135075. 
19813557. 
20511149. 
21228253. 
21965275. 
22722628. 
23500728. 
24300000. 
26393634. 

28.4 
28.6 
28.8 
29.0 
29.2 
29.4 
29.6 
29.8 
30.0 
30.5 

28629151. 
31013642. 
33554432. 
36259082. 
39135393. 
42191410. 
45435424. 
48875980. 
52521875. 
56382167. 

31.0 
31.5 
32.0 
32.5 
33.0 
33.5 
34.0 
34.5 
35.0 
35.5 

60466176.   36.0 
64783487.   36.5 
69343957.   37.0 
74157715.   37.5 
79235168.   38.0 
84587005.   38.5 
90224199.   39.0 
96158012.   39.5 
102400000.   40.0 

_  J 

tf°  !  ^ 

NATIONAL  TUBE  COMPANY.                     281 

Squares,  Cubes,  Square  Roots,  Cube  Roots,  Logarithms,  Re- 
ciprocals, Circumferences  and  Circular  Areas 
of  Nos.  from  \  to  JOOO. 

(FROM  CARNEGIE  HAND  BOOK.) 

No. 

1 
2 
3 
4 
5 

Sq. 

1 
4 
9 
16 
25 

Cube. 

Square 
Root. 

Cube 
Root. 

Log. 

1000 
X 
Recip. 

No.  =  Dia. 

Circ'm 

Area. 

1 
8 
27 
64 
125 

1.0000 
1.4142 
1.7321 
2.0000 
2.2361 

1.0000 
1.2599 
1.4422 
1.5874 
1.7100 

0.00000 
0.30103 
0.47712 
0.60206 
0.69897 

1000.000 
500.000 
333.  333 
250.000 
200.000 

3.142 
6.283 
9.425 
12.566 
15.708 

0.7854 
3.1416 
7.0686 
12.5664 
19.6350 

6 
7 
8 
9 
10 

36 
49 
64 
81 
100 

216 
343 
512 
729 
1000 

2.4495 
2.6458 
2.8284 
3.0000 
3.1623 

1.8171 
1.9129 
2.0000 
2.0801 
2.1544 

0.77815 
0.84510 
0.90309 
0.95424 
1.00000 

166.667 
142.857 
125.000 
111.111 
100.000 

18.850 
21.991 

25.133 

28.274 
31.416 

28.2743 
38.4845 
50.2655 
63.6173 
78.5398 

11 
12 
13 
14 
15 

121 
144 
169 
196 
225 

1331 

1728 
2197 
2744 
3375 

3.3166 
3.4641 
3.6056 
3.7417 
3.8730 

2.2240 
2.2894 
2.3513 
2.4101 
2.4662 

1.04139 
1.07918 
1.11394 
1.14613 
1.17609 

90.9091 
83.3333 
76.9231 
71.4286 
66.6667 

34.558 
37.699 
40.841 
43.982 
47.124 

95.0332 
113.097 
132.732 
153.938 
176.715 

16 
17 
18 
19 
20 

256 
289 
324 
361 
400 

4096 
4913 
5832 
6859 
8000 

4.0000 
4.1231 
4.2426 
4.3589 
4.4721 

2.5198 
2.5713 
2.6207 
2.6684 
2.7144 

1.20412 
1.23045 
1.25527 

1.27875 
1.30103 

62.5000 
58.8235 
55.5556 
52.6316 
50.0000 

50.265 
53.407 
56.549 
59.690 
62.832 

201.062 
226.980 
254.469 
283.529 
314.159 

21 
22 
23 
24 
25 

441 

484 
529 
576 
625 

9261 
10648 
12167 
13824 
15625 

4.5826 
4.6904 
4.7958 
4.8990 
5.0000 

2.7589 
2.8020 
2.8439 
2.8845 
2.9240 

1.32222 
1.34242 
1.36173 
1.38021 
1.39794 

47.6190 
45.4545 
43.4783 
41.6667 
40.0000 

65.973 
69.115 
72.257 
75.398 
78.540 

346.361 
380.133 
415.476 
452.389 
490.874 

26 
27 
28 
29 
30 

676 

729 
784 
841 
900 

17576 
19083 
21952 
24389 
27000 

5.0990 
5.1962 
5.2915 
5.3852 
5.4772 

2.9625 
3.0000 
3.0366 
3.0723 
3.1072 

.41497 
.43136 
.44716 
.46240 
.47712 

38.4615 
37.0370 
35.7143 
34.4828 
33.3333 

81.681 
84.823 
87.965 
91.106 
94.248 

530.929 
572.555 
615.752 
660.520 
706.858 

31 
32 
33 
34 
35 

961 
1024 
1089 
1156 
1225 

29791 
32768 
35937 
39304 
42875 

5.5678 
5.6569 
5.7446 
5.8310 
5.9161 

3.1414 
3.1748 
3.2075 
3.2396 
3.2711 

1.49136 
1.50515 
1.51851 
1.53148 
1.54407 

32.2581 
31.2500 
30.3030 
29.4118 
28.5714 

97.389 
100.531 
103.673 
106.814 
109.956 

754.768 
804.248 
855.299 
907.920 
962.113 

36 
37 
38 
39 
40 

1296 
1369 
1444 
1521 
1600 

46656 
50653 
54872 
59319 
64000 

6.0000 
6.0828 
6.1644 
6.2450 
6.3246 

3.3019 
3.3322 
3.8620 
3.3912 
3.4200 

1.55630 
1.56820 
1.57978 
1.59106 
1.60206 

27.7778 
27.0270 
26.3158 
25.6410 
25.0000 

113.097 
116.239 
119.381 
122.522 
125.66 

1017.88 
1075.21 
1134.11 
1194.59 
1256.64 

41 
42 
43 
44 
45 

1681 
1704 
1849 
1936 
2025 

68921 
74088 
79507 
85184 
91125 

6.4031 
6.4807 
6.5574 
6.6332 
6.7082 

3.4482 
3.4760 
3.5034 
3.5303 
3.5569 

1.61278 
1.62325 
1.63347 
1.64345 
1.65321 

24.3902 
23.8095 
23.2558 
22.7273 
22.2222 

128.81 
131.95 
135.09 
138.23 
141.37 

1320.25 
1385.44 
1452.20 
1520.53 
1590.43 

282                      NATIONAL  TUBE  COMPANY. 

Squares,  Cubes,  Square  Roots,  Cube  Roots,  Logarithms,  Etc. 

(CONTINUED.) 

No 

Sq. 

2116 
2209 
2304 
2401 

Cube. 

Square 
Root. 

Cube 
Root. 

Log. 

1000 
X 
Recip. 

No   =  Dia. 

Circ'm 

Area. 

46 
47 
48 
49 

97336 
103823 
110592 
117649 

6.7823 
6.8557 
6.9282 
7.0000 

3.5aso 

3.6088 
3.6342 
3.6593 

1.66276 
1.67210 
1.68124 
1.69020 

21.7391 
21.2766 
20.8333 
20.4088 

144.51 
147.65 
150.80 
153.94 

1661.90 
1734.94 
1809.56 
1885.74 

50 
51 
52 
53 
54 

2500 
2601 
2704 
2809 
2916 

125000 
132651 
140608 
148877 
157464 

7.0711 
7.1414 
7.2111 
7.2801 
7.3485 

3.6840 
3.7084 
3.7325 
3.7563 
3.7798 

1.69897 
1.70757 
1.71600 
1.72428 
1.73239 

20.0000 
19.6078 
19.2308 
18.8679 
18.5185 

157.08 
160.22 
163.36 
166.50 
169.65 

1963.50 
2042.82 
2123.72 
2206.18 
2290.22 

55 
56 

57 
58 
59 

3025 
3136 
3249 
3364 
3481 

166375 
175616 
185193 
195112 
205379 

7.4162 
7.4833 
7.5498 
7.6158 
7.6811 

3.8030 
3.8259 
3.8485 
3.8709 
3.8930 

1.74036 
1.74819 
1.75587 
1.76343 
1.77085 

18.1818 
17.8571 
17.5439 
17.2414 
16.9492 

172.79 
175.93 
179.07 
182.21 
185.35 

2375.83 
2463.01 
2551.76 
2642.08 
2733.97 

60 
61 
62 
63 
64 

3600 
3721 
3844 
3969 
4096 

216000 
226981 
238328 
250047 
262144 

7.7460 
7.8102 
7.8740 
7.9373 
8.0000 

3.9149 
3.9365 
3.9579 
3.9791 
4.0000 

1.77815 
1.78533 
1.79239 
1.79934 
1.80618 

16.6667 
16.3934 
16.1290 
15.8730 
15.6250 

188.50 
191.64 
194.78 
197.92 
201.06 

2827.43 
2922.47 
3019.07 
3117.25 
3216.99 

65 
66 
67 
68 
69 

4225 
4356 
4489 
4624 
4761 

274625 
287496 
300763 
314432 
328509 

8.0623 
8.1240 
8.1854 
8.2462 
8.3066 

4.0207 
4.0412 
4.0615 
.0817 
.1016 

1.81291 
1.81954 
1.82607 
1.83251 
1.83885 

15.3846 
15.1515 
14.9254 
14.7059 
14.4928 

204.20 
207.35 
210.49 
213.63 
216.77 

3318.31 
3421.19 
3525.65 
3631.68 
3739.28 

70 
71 
72 
73 

74 

4900 
5041 
5184 
5329 
5476 

343000 
357911 
373248 
389017 
405224 

8.3666 
8.4261 
8.4853 
8.5440 
8.6023 

.1213 
.1408 
.1602 
.1793 
.1983 

1.84510 
1.85126 
1.85733 
1.86332 
1.86923 

14.2857 
14.0845 
13.8889 
13.6986 
13.5135 

219.91 
223.05 
226.19 
229.34 
232  48 

3848.45 
3959.19 
4071.50 
4185.39 
4300.84 

75 
76 

77 
78 
79 

5625 
5776 
5929 
6084 
6241 

421875 
438976 
456533 
474552 
493039 

8.6603 

8.7178 
8.7750 
8.8318 
8.8882 

4.2172 

4.2a58 
4.2543 
4.2727 
4.2908 

1.87506 
1.88081 
1.88649 
1.89209 
1.89763 

13.3333 
13.1579 
12.9870 
12.8205 
12.6582 

235.62 
238.76 
241.90 
245.04 
248.19 

4417.86 
4536.46 
4656.63 
4778.36 
4901.67 

80 
81 
82 
83 
84 

6400 
6561 
6724 
6889 
7056 

512000 
531441 
551368 
571787 
592704 

8.9443 
9.0000 
9.0554 
9.1104 
9.1652 

4.3089 
4.3267 
4.3445 
4.3621 
4.3795 

1.90309 
1.90849 
1.91381 
1.91908 
1.92428 

12.5000 
12.3457 
12.1951 
12.0482 
11.9048 

251.33 
254.47 
257.61 
260.75 
263.89 

5026.55 
5153.00 
5281.02 
5410.61 
5541.77 

85 
86 
87 
88 
89 

7225 
7396 
7569 

7744 
7921 

614125 
636056 
658503 
681472 
704969 

9.2195 
9.2736 
9.3274 
9.3808 
9.4340 

4.3968 
4.4140 
4.4310 
4.4480 
4.4647 

.92942 
.93450 
.93952 
.94448 
.94939 

11.7647 
11.6279 
11.4943 
11.3636 
11.2360 

267.04 
270.18 
273.32 
276.46 
279.60 

5674.50 
5808.80 
5944.68 
6082.12 
6221.14 

NATIONAL  TUBE  COMPANY.                     283 

Squares,  Cubes,  Square  Roots,  Cube  Roots,  Logarithms,  Etc. 

(CONTINUED.) 

No. 

90 
91 
92 
93 
94 

Sq. 

Cube. 

Square 
Root. 

Cube 
Root. 

Log. 

1000 
X 
Recip. 

No.  =  Dia. 

Circ'm 

Area. 

8100 
8281 
8464 
8649 
8836 

729000 
753571 
778688 
804357 
830584 

9.4868 
9.5394 
9.5917 
9.6437 
9.6954 

4.4814 
4.4979 
4.5144 
4.5307 
4.5468 

1.95424 
1.95904 
1.96379 
1.96848 
1.97313 

11.1111 
10.9890 
10.8696 
10.7527 
10.6383 

282.74 
285.88 
289.03 
292.17 
295.31 

6361.73 
6503.88 
6647.61 
6792.91 
6939.78 

95 
96 
97 
98 
99 

9025 
9216 
9409 
9604 
9801 

857375 
884736 
912673 
941192 
970299 

9.7468 
9.7980 
9.8489 
9.8995 
9.9499 

4.5629 
4.5789 
4.5947 
4.6104 
4.6261 

1.97772 
1.98227 
1  98677 
1.99123 
1.99564 

10.5263 
10.4167 
10.3093 
10.2041 
10.1010 

298.45 
301.59 
304.73 
307.88 
311.02 

7088.22 
7238.23 
7389.81 
7542.96 
7697.69 

100 
101 
102 
103 
104 

10000 
10201 
10404 
10609 
10816 

1000000 
1030301 
1061208 
1092727 
1124864 

10.0000 
10.0499 
10.0995 
10.1489 
10.1980 

4.6416 
4.6570 
4.6723 
4.6875 
4.7027 

2.00000 
2.00432 
2.00860 
2.01284 
2.01703 

10.0000 
9.90099 
9.80392 
9.70874 
9.61538 

314.16 
317.30 
320.44 
323.58 
326.73 

7853.98 
8011.85 
8171.28 
8332.29 

8494.87 

105 
106 
107 
108 
109 

11025 
11236 
11449 
11664 
11881 

1157625 
1191016 
1225043 
1259712 
1295029 

10.2470 
10.2956 
10.3441 
10.8923 
10.4403 

4.7177 
4.7326 
.7475 
.7622 
.7769 

2.02119 
2.02531 
2.02938 
2.03342 
2.03743 

9.52381 
9.43396 
9.34579 
9.25926 
9.17431 

329.87 
333.01 
336.15 
339.29 
342.43 

8659.01 
8824.73 
8992.02 
9160.88 
9331.32 

110 
111 
112 
113 
114 

12100 
12321 
12544 
12769 
12996 

1331000 
1367631 
1404928 
1442897 
1481544 

10.4881 
10.5357 
10.5830 
10.6301 
10.6771 

.7914 
.8059 
4.8203 
4.8346 
4.8488 

2.04139 
2.04532 
2.04922 
2.05308 
2.05690 

9.09091 
9.00901 
8.92857 
8.84956 
8.77193 

345.58 
348.72 
351.86 
355.00 
358.14 

9503.32 
9676.89 
9852.03 
10028.7 
10207.0 

115 
116 
117 
118 
119 

13225 
13456 
13689 
13924 
14161 

1520875 
1560896 
1601613 
1643032 
1685159 

10.7238 
10.7703 
10.8167 
10.8628 
10.9087 

4.8629 
4.8770 
3.8910 
4.9049 
4.9187 

2.06070 
2.06446 
2.06819 
2.07188 
2.07555 

8.69565 
8.62069 
8.54701 
8.47458 
8.40336 

361.28 
364.42 
367.57 
370.71 
373.85 

10386.9 
10568.3 
10751.3 
10935.9 
11122.0 

120 
121 
122 
123 
124 

14400 
14641 
14884 
15129 
15376 

1728000 
1771561 
1815848 
1860867 
1906624 

10.9545 
11.0000 
11.0454 
11.0905 
11.1355 

4.9324 
4.9461 
4.9597 
4.9732 
4.9866 

2.07918 
2.08279 
2.08636 
2.08991 
2.09342 

8.33333 
8.26446 
8.19672 
8.13008 
8.06452 

376.99 
380.13 
383.27 
386.42 
389.56 

11309.7 
11499.0 
11689.9 
11882.3 
12076.3 

125 
126 
127 
128 
129 

15625 
15876 
16129 
16384 
16641 

1953125 
2000376 
2048383 
2097152 
2146689 

11.1803 
11.2250 
11.2694 
11.3137 
11.3578 

5.0000 
5.0133 
5.0265 
5.0397 
5.0528 

2.09691 
2.10037 
2.10380 
2.10721 
2.11059 

8.00000 
7.93651 
7.87402 
7.81250 
7.75194 

392.70 
395.84 
398.98 
402.12 
405.27 

12271.8 
12469.0 
12667.7 
12868.0 
13069.8 

130 
131 
132 
133 
134 

16900 
17161 
17424 
17689 
17956 

2197000 
2248091 
2299968 
235263? 
2406104 

11.4018 
11.4455 
11.4891 
11.5326 
11.5758 

5.0658 
5.0788 
5.0916 
5.1045 
5.1172 

2.11394 
2.11727 
2.12057 
2.12385 
2.12710 

7.69231 
7.63359 
7.57576 
7.51880 
7.46269 

408.41 
411.55 
414.69 
417.83 
420.97 

13273.2 
13478.2 
13684.8 
13892.9 
14102.6 

L  , 

284                     NATIONAL  TUBE  COMPANY. 

Squares,  Cubes,  Square  Roots,  Cube  Roots,  Logarithms,  Etc. 

(CONTINUED.) 

No 

Sq. 

Cube. 

Square 
Root. 

Cube 
Root. 

Log. 

1000 
X 
Recip. 

No.  =    Dia. 

Circ'm 

Area. 

135 
136 
137 
138 
139 

1822 
1849 
1876 
19044 
1932 

246037 
251545 
257135 
262807 
268561 

11.619 
11.661 
11.704 
11.747 
11.789 

5.129S 
5.1426 
5.1551 
5.1676 
5.1801 

2.1303 
2.1335 
2.1367 
2.1398 
2.1430 

7.40741 
7.35294 
7.29927 
7.2463S 
7.19424 

424.1 
427.2 
430.4 
433.5 
436.6 

14313.9 
14526.7 
14741.1 
14957.1 
15174.7 

140 
141 
142 
143 
144 

19600 
19881 
20164 
20449 
20736 

2744000 
280322 
2863288 
2924207 
2985984 

11.832 
11.874 
11.9164 
11.958 
12.0000 

5.1925 
5.204 
5.217 
5.229 
5.2415 

2.1461 
2.1492 
2.1522 
2.1553 
2.1583 

7.14286 
7.0922 
7.0422 
6.9930 
6.9444 

439.8 
442.9 
446.1 
449.2 
452.3 

15393.8 
15614.5 
15836.8 
16060.6 
16286.0 

145 
146 
147 
148 
149 

21025 
21316 

21609 
21904 
22201 

3048625 
3112136 
3176523 
3241792 
3307949 

12.041 
12.0830 
12.1244 
12.1655 
12.2066 

5.2536 
5.265b 
5.2776 
5.2896 
5.3015 

2.16137 
2.16435 
2.16732 
2.17026 
2.17319 

6.89655 
6.84932 
6.80272 
6.75676 
6.71141 

455.5 
458.6 
461.8 
464.96 
468.10 

16513.0 
16741.5 
16971.7 
17203.4 
17436.6 

150 
151 
152 
153 

154 

22500 
22801 
23104 
23409 
23716 

3375000 
3442951 
3511808 
3581577 
3652264 

12.2474 
12.2882 
12.3288 
12.3693 
12.4097 

5.3133 
5.3251 
5.3368 
5.3485 
5.3601 

2.17609 
2.17898 
2.18184 
2.18469 
2.18752 

6.66667 
6.62252 
6.57895 
6.53595 
6.49351 

471.24 
474.38 
477.52 
480.66 
483.81 

17671.5 
17907.9 
18145.8 
18385.4 
18626.5 

155 
156 
157 
158 
159 

24025 
24336 
24649 
24964 
25281 

3723875 
3796416 
3869893 
3944312 
4019679 

12.4499 
12.4900 
12.5300 
12.5698 
12.6095 

5.3717 
5.3832 
5.3947 
5.4061 
5.4175 

2.19033 
2.19312 
2.19590 
2.19866 
2.20140 

6.45161 
6.41026 
6.3(5943 
6.32911 
6.28931 

486.95 
490.09 
493.23 
496.37 
499.51 

18869.2 
19113.4 
19359.3 
19606.7 
19855.7 

160 
161 
162 
163 
164 

25600 
25921 
26244 
26569 
26896 

4096000 
4173281 
4251528 
4330747 
4410944 

12.6491 
12.6886 
12.7279 
12.7671 
12.8062 

5.4288 
5.4401 
5.4514 
5.4626 
5.4737 

2.20412 
2.20683 
2.20952 
2.21219 
2.21484 

6.25000 
6.21118 
6.17284 
6.13497 
6.09756 

502.65 
505.80 
508.94 
512.08 
515.22 

20106.2 
20358.3 
20612.0 
20867.2 
21124.1 

165 
166 
167 
168 
169 

27225 
27556 
27889 
28224 
285C1 

4492125 
4574296 
4657463 
4741632 
4826809 

12.8452 
12.8841 
12.9228 
12.9615 
13.0000 

5.4848 
5.4959 
5.5069 
5.5178 
5.5288 

2.21748 
2.22011 
2.22272 
2.22531 

2.22789 

6.06061 
6.02410 
5.98802 
5.95238 
5.91716 

518.36 
521.50 
524.65 
527.79 
530.93 

21382.5 
21642.4 
21904.0 
22167.1 
22431.8 

170 
171 
172 
173 

174 

28900 
29241 
29584 
29929 
30276 

4913000 
5000211 
5088448 
5177717 
5268024 

13.0384 
13.0767 
13.1149 
13.1529 
13.1909 

5.5397 
5.5505 
5.5613 
5.5721 

5.5828 

2.23045 
2.23300 
2.23553 
2.23805 
2.24055 

5.88235 
5.84795 
5.81395 
5.78035 
5.74713 

534.07 
537.21 
540.35 
543.50 
546.64 

22698.0 
22965.8 
23235.2 
23506.2 
23778.7 

175 
176 
177 
178 
179 

30625 
30976 
31329 
31684 
32041 

5359375 
5451776 
5545233 
5639752 
5735339 

13.2288 
13.2665 
13.3041 
13.3417 
13.3791 

5.5934 
5.6041 
5.0147 
5.6252 
5.6357 

2.24304 
2.24551 
2.24797 
2.25042 
2.25285 

5.71429 
5.68182 
5.64972 
5.61798 
5.58659 

549.78 
552.92 
556.06 
559.20 
562.35 

24052.8 
24328.5 
24605.7 
24884.6 
25164.9 

NATIONAL  TUBE  COMPANY.                       285 

Squares,  Cubes,  Square  Roots,  Cube  Roots,  Logarithms,  Etc. 

(CONTINUED.) 

No. 

180 
181 
182 
183 
184 

Sq. 

Cube. 

Square 
Root. 

Cube 
Root. 

Log. 

1000 
X 
Recip. 

No.   =     Dia. 

Circ'm 

Area. 

32400 
32761 
33124 
33489 
33856 

5832000 
5929741 
6028568 
6128487 
6229504 

13.4164 
13.4536 
13.4907 
13.5277 
13.5647 

5.6462 
5.6567 
5.6671 
5.6774 
5.6877 

2.25527 

2.25768 
2.26007 
2.26245 
2.26482 

5.55556 
5.52486 
5.49451 
5.46448 
5.43478 

565.49 
568.63 
571.77 
574.91 
578.05 

25446.9 
25730.4 
26015.5 
26302.2 
26590.4 

186 
186 
187 
188 
189 

34225 
34596 
34969 
35344 
35721 

6331625 
6434856 
6539203 
6644672 
6751269 

13.6015 
13.6382 
13.6748 
13.7113 
13.7477 

5.69PO 
5  7083 
5.7185 

5.7287 
5.7388 

2.26717 
2.26951 

2.27184 
2.27416 
2.27646 

5.40541 
5.37634 
5.34759 
5.31915 
5.29101 

581.19 
584.34 
587.48 
590.62 
593.76 

26880.3 
27171.6 
27464.6 
27759.1 
28055.2 

190 
191 
192 
193 
194 

36100 
36481 
36864 
37249 
37636 

6859000 
6967871 
7077888 
7189057 
7301384 

13.7840 
13.8203 
13.8564 
13.8924 
13.9284 

5.7489 
5.7590 
5.7690 
5.7790 
5.7890 

2.27875 
2.28103 
2.28330 
2.28556 
2.28780 

5.26316 
5.23560 
5.20833 
5.18135 
5.15464 

596.90 
600.04 
603.19 
606.33 
609.47 

28352.9 
28652.1 
28952.9 
29255.3 
29559.2 

195 
196 
197 
198 
199 

38025 

38416 
38809 
39204 
39601 

7414875 
7529536 
7645373 
7762392 
7880599 

13.9642 
14.0000 
14.0357 
14.0712 
14.1067 

5.7989 
5.8088 
5.8186 
5.8285 
5.8383 

2.29003 
2.29226 
2.29447 

2.29667 
2.29885 

5.12821 
5.10204 
6.07614 
5.05051 
5.02513 

612.61 
615.75 
618.89 
622.04 
625.18 

29864.8 
30171.9 
30480.5 
30790.7 
31102.6 

200 
201 
202 
203 
204 

40000 
40401 
40804 
41209 
41616 

8000000 
8120601 
8242408 
8365427 
8489664 

14.1421 
14.1774 
14.2127 
14.2478 
14.2829 

5.8480 

5.8578 
5.8675 
5.8771 
5.8868 

2.30103 
2.30320 
2.30535 
2.30750 
2.30963 

5.00000 
4.97512 
4.95050 
4.92611 
4.90196 

628.32 
631.46 
634.60 
637.74 
640.89 

31415.9 
31730.9 
32047.4 
32365.5 
32685.1 

205 
206 
207 
208 
209 

42025 
42436 
42849 
43264 
43681 

8615125 
8741816 
8869743 
8998912 
9129329 

14.3178 
14.3527 
14.3875 
14.4222 
14.4568 

5.8964 
5.9059 
5.9155 
5.92(50 
5.9345 

2.31175 
2.31387 
2.31597 
2.31806 
2.32015 

4.87805 
4.85437 
4.83092 
4.80769 
4.78469 

644.03 
647.17 
650.31 
653.45 
656.59 

33006.4 
33329.2 
33653.5 
33979.5 
34307.0 

210 
211 
212 
213 

214 

44100 
44521 
44944 

45369 
45796 

9261000 
9393931 
95-28128 
96(>3597 
9800344 

14.4914 
14.5258 
14.560-2 
14.5945 
14.6287 

5.9439 
5.9533 
5.9627 
5.9721 
5.9814 

2.32222 

2.32428 

2  !  32838 
2.33041 

4.76190 
4.73934 
4.71698 
4.69484 
4.67290 

659.73 
662.88 
666.02 
669.16 
672.30 

34636.1 
34966.7 
35298.9 
35632.7 
35968.1 

215 
216 
217 
218 
219 

46225 
46656 
47089 
47524 
47961 

9938375 
10077696 
10218313 
10360232 
10503459 

14.6629 
14.6969 
14.7309 
14.7648 
14.7986 

5.9907 
6.0000 
6.0092 
6.0185 
6.0277 

2.33244 
2.33445 
2.  ,33646 
2.338-16 
2  34044 

4.65116 
4.62963 
4.60829 
4.58716 
4.56621 

675.44 

678.58 
681.73 
684.87 
688.01 

36305.0 
36643.5 
36983.6 
37325.3 
37668.5 

220 
221 
222 
223 
224 

48400 
48841 
49284 
49729 
5017( 

10648000 
10793861 
10941048 
11089567 
11239424 

14.8324 
14.8661 
14.8997 
14.9332 
14.9666 

6.0368 
6  0459 
6.0550 
6.0641 
6.0732 

2.34242 
2.34439 
2.34635 
2.34&30 
2.35025 

4.54545 
4.52489 
4.50450 
4.48431 
4.46429 

691.15 
694.29 
697.43 
700.58 
703.72 

38013.3 
38359.6 
38707.6 
39057.1 
39408.1 

t 

<3 

286                    NATIONAL  TUBE  COMPANY. 

Squares,  Cubes,  Square  Roots,  Cube  Roots,  Logarithms,  Etc. 

(CONTINUED.) 

No. 

Sq. 

Cube. 

Square 
Root. 

Cube 
Root. 

Log. 

1000 
X 
Recip. 

No    =  Dia. 

Circ'm 

Area. 

225 

50625 

11390625 

15.0000 

6.0822 

2.35218 

4.44444 

706.86 

39760.8 

226 

51076 

11543176 

15.0333 

6.0912 

2.35411 

4.42478 

710.00 

40115.0 

227 

51529 

11697083 

15.0665 

6.1002 

2.35603 

4.40529 

713.14 

40470.8 

228 

51984 

11852352 

15.0997 

6.1091 

2.35793 

4.38596 

716.28 

40828.1 

229 

52441 

12008989 

15.1327 

6.1180 

2.35984 

4.36681 

719.42 

41187.1 

230 

52900 

12167000 

15.1658 

6.1269 

2.36173 

4.34783 

722.57 

41547.6 

231 

53361 

12326391 

15.1987 

6.1358 

2.36361 

4.32900 

725.71 

41909.6 

232 

53824 

12487168 

15.2315 

6.1446 

2.36549 

4.31034 

728.85 

42273.3 

233 

54289 

12649337 

15.2643 

6.1534 

2.36736 

4.29185 

731.99 

42638.5 

234 

54756 

12812904 

15.2971 

6.1622 

2.36922 

4.27350 

735.13 

43005.3 

235 

55225 

12977875 

15.3297 

6.1710 

2.37107 

4.25532 

738.27 

43373.6 

236 

55696 

13144256 

15.3623 

6.1797 

2.37291 

4.23729 

741.42 

43743.5 

237 

56169 

13312053 

15.3948 

6.1885 

2.37475 

4.21941 

744.56 

44115.0 

238 

56644 

13481272 

15.4272 

6.1972 

2.37658 

4.20168 

747.70 

44488.1 

239 

57121 

13651919 

15.4596 

6.2058 

2.37840 

4.18410 

750.84 

44862.7 

240 

57600 

13824000 

15.4919 

6.2145 

2.38021 

4.16667 

753.98 

45238.9 

241 

58081 

13997521 

15.5242 

6.2231 

2.38202 

4.14938 

757.12 

45616.7 

242 

58564 

14172488 

15.5563 

6.2317 

2.38382 

4.13223 

760.27 

45996.1 

243 

59049 

14348907 

15.5885 

6.2403 

2.38561 

4.11523 

763.41 

46377.0 

244 

59536 

14526784 

15.6205 

6.2488 

2.38739 

4.09836 

766.55 

46759.5 

245 

60025 

14706125 

15.6525 

6.2573 

2.38917 

4.08163 

769.69 

47143.5 

246 

60516 

14886936 

15.6844 

6.2658 

2.39094 

4.06504 

772.83 

47529.2 

247 

61009 

15069223 

15.7162 

6.2743 

2.39270 

4.04858 

775.97 

47916.4 

248 

61504 

15252992 

15.7480 

6.2828 

2.39445 

4  03226 

779.12 

48305.1 

249 

62001 

15438249 

15.7797 

6.2912 

2.39620 

4.01606 

782.26 

48695.5 

250 

62500 

15625000 

15.8114 

6.2996 

2.39794 

4.00000 

785.40 

49087.4 

251 

63001 

15813251 

15.8430 

6.3080 

2.39967 

3.98406 

788.54 

49480.9 

252 

63504 

16003008 

15.8745 

6.3164 

2.40140 

3.96825 

791.68 

49875.9 

253 

64009 

16194277 

15.9060 

6.3247 

2.40312 

3.95257 

794.82 

50272.6 

254 

64516 

16387064 

15.9374 

6.3330 

2.40483 

3.93701 

797.96 

50670.7 

255 

65025 

16581375 

15.9687 

6.3413 

2.40654 

3.92157 

801.11 

51070.5 

256 

65536 

16777216 

16.0000 

6.3496 

2.40824 

3.90625 

804.25 

51471.9 

257 

66049 

16974593 

16.0312 

6.3579 

2.40993 

3.89105 

807.39 

51874.8 

258 

66564 

17173512 

16.0624 

6.3661 

2.41162 

3.87597 

810.53 

52279.2 

259 

67081 

17373979 

16.0935 

6.3743 

2.41330 

3.86100 

813.67 

52685.3 

260 

67600 

17576000 

16.1245 

6.3825 

2.41497 

3.84615 

816.81 

53092.9 

261 

68121 

17779581 

16.1555 

6.3907 

2.41664 

3.83142 

819.96 

53502.1 

262 

68644 

17984728 

16.1864 

6.3988 

2  41830 

3.81679 

823.10 

53912.9 

263 

69169 

18191447 

16.2173 

6.4070 

2.41996 

3.80228 

826.24 

54325.2 

264 

69696 

18399744 

16.2481 

6.4151 

2.42160 

3.78788 

829.38 

54739.1 

265 

70225 

18609625 

16.2788 

6.4232 

2.42325 

3.77358 

832  52 

55154.6 

266 

70756 

18821096 

16.8095 

6.4312 

2.42488 

3.75940 

835.66 

55571.6 

267 

71289 

19034163 

16.3401 

(5.4393 

2.42651 

3.74532 

838.81 

55990.3 

268 

71824 

19248832 

16.3707 

6.4473 

2.42813 

3.73134 

841.95 

50410.4 

269 

72361 

19465109 

16.4012 

6.4553 

2.42975 

3.71747 

845.  C9 

56832.2 

NATIONAL  TUBE  COMPANY.                       287 

1    Squares,  Cubes,  Square  Roots,  Cube  Roots,  Logarithms,  Etc. 

(CONTINUED.) 

1      No. 

Sq. 

Cube. 

Square 
Root. 

Cube 
Root. 

LOR. 

1000 
X 
Recip. 

No.  =  Dla. 

Circ'm 

Area. 

1     270 
1      271 
1      272 
1     273 
I     274 

72900 
73441 
73984 
74529 
75076 

19683000 
19902511 
20123648 
20346417 
20570824 

16  4317 
16.4621 
16.4924 
16.5227 
16.5529 

6.4633 
6.4713 

6.4792 
6.4872 
6.4951 

2.43136 
2.43297 
2.43457 
2.43616 
2.43775 

3.70370 
3.69004 
3.67647 
3.66300 
3.64964 

848.23 
851.37 
854.51 
857.66 
860.80 

57255.5 

57680.4 
58106.9 
58534.9 
58964.6 

1     275 
1      276 
1     277 
I     278 
1     279 

75625 
76176 
76729 
77284 
77841 

20796875 
21024576 
21253933 
21484952 
21717639 

16.5831 
16.6132 
16.6433 
16.6733 
16.7033 

6.5030 
6.5108 
6.5187 
6.5265 
6.5343 

2.43933 
2.44091 
2.44248 
2.44404 
2.44560 

3.63636 
3.62319 
3.61011 
3.59712 
3.58423 

863.94 
867.08 
870.22 
873.36 
876.50 

59395.7 
59828.5 
60262.8 
60698.7 
61136.2 

1     280 
1     281 
1      282 
1     283 
1     234 

78400 
78961 
79524 
80089 
80656 

21952000 
22188041 
22425768 
22665187 
22906304 

16.7332 
16.7631 
16.7929 
16.8226 
16.8523 

6.5421 
6.5499 
6.5577 
6.5654 
6.5731 

2.44716 
2.44871 
2.45025 
2.45179 
2.45332 

3.57143 
3.55872 
3.54610 
3.53357 
3.52113 

879.65 
882.79 
885.93 
889.07 
892.21 

61575.2 
62015.8 
62458.0 
62901.8 
63347.1 

1     285 

286 
287 
288 
289 

81225 
81796 
82369 
82944 
83521 

23149125 
23393656 
23639903 
23887872 
24137569 

16.8819 
16.9115 
16.9411 
16.9706 
17.0000 

6.5808 
6.5885 
6.5962 
6.6039 
6.6115 

2.45484 
2.45637 
2.45788 
2.45939 
2.46090 

3.50877 
3.49650 
3.48432 
3.47222 
3.46021 

895.35 
898.50 
901.64 
904.78 
907.92 

63794.0 
64242.4 
64692.5 
65144.1 
65597.2 

290 
291 
292 
293 
294 

84100 
84681 
85264 
85849 
86436 

24389000 
24642171 
24897088 
25153757 
25412184 

17.0294 
17.0587 
17.0880 
17.1172 
17.1464 

6.6191 
6.6267 
6.6343 
6.6419 
6.6494 

2.46240 
2.46389 
2.46538 
2.46687 
2.46835 

3.44828 
3.43643 
3.42466 
3.41297 
3.40136 

911.06 
914.20 
917.35 
920.49 
923.63 

66052.0 
66508.3 
66966.2 
67425.6 
67886.7 

295 

296 
297 
298 
299 

87025 
87616 
88209 
88804 
89401 

25672375 
25934336 
26198073 
26463592 
26730899 

17.1756 
17.204? 
17.2337 
17.2627 
17.2916 

6.6569 
6.6644 
6.6719 
6.6794 
6.6869 

2.46982 
2.47129 
2.47276 
2.47422 
2.47567 

3.38983 
3.37838 
3.36700 
3.35570 
3.34448 

926.77 
929.91 
933.05 
936.19 
939.34 

68349.3 
68813.5 
69279.2 
69746.5 
70215.4 

300 
301 
302 
303 
304 

90000 
90601 
91204 
91809 
92416 

27000000 
27270901 
27543608 
27818127 
28094464 

17.3205 
17.3494 
17.3781 
17.4069 
17.4356 

6.6943 
6.7018 
6.7092 
6.7166 
6.7240 

2.47712 
2.47857 
2.48001 
2.48144 
2.48287 

3.33333 
3.32226 
3.31126 
3.30033 
3.28947 

942.48 
945.62 
948.76 
951.90 
955.04 

70685.8 
71157.9 
71631.5 
72106.6 
72583.4 

305 
306 
307 
308 
309 

93025 
93636 
94249 
94864 
95481 

28372625 
28652616 
28934443 
29218112 
29503629 

17.4642 
17.4929 
17.5214 
17.5499 
17.5784 

6.7313 
6.7387 
6.7460 
6.7533 
6.7606 

2.48430 
2.48572 
2.48714 
2.48855 
2.48996 

3.27869 
3.26797 
3.25733 
3.24675 
3.23625 

958.19 
961.33 
964.47 
967.61 
970.75 

73061.7 
73541.5 
74023.0 
74506.0 
74990.6 

310 
311 
312 
313 
314 

96100 
96721 
97344 
97969 
98596 

29791000 
30080231 
30371328 
30664297 
30959144 

17.6068 
17.6352 
17.6635 
17.6918 
17.7200 

6.7679 
6.7752 
6.7824 
6.7897 
6.7969 

2.49136 
2.49276 
2.49415 
2.49554 
2.49693 

3.22581 
3.21543 
3.20513 
3.19489 
3.18471 

973.89 
977.04 
980.18 
983.32 
986.46 

75476.8 
75964.5 
76453.8 
76944.7 
77437.1 

n  ,', 

288                      NATIONAL  TUBE  COMPANY, 

Squares,  Cubes,  Square  Roots,  Cube  Roots,  Logarithms,  Etc. 

(CONTINUED.) 

No 

Sq. 

Cube. 

Square 
Root. 

Cube 

Root. 

Log. 

1000 
X 
Recip 

No   =  Dia. 

Circ'm 

Area. 

315 

99225 

31255875 

17.7482 

6.8041 

2.49831 

3.17460 

989.60 

77931.1 

316 

99856 

31554496 

17.7764 

6.8113 

2.49969 

3.16456 

992.74 

78426.7 

317 

100489 

31855013 

17.8045 

6.8185 

2.50106 

3.15457 

995.88 

78923.9 

318 

101124 

32157432 

17.8326 

6.8256 

2.50243 

3.14465 

999.03 

79422.6 

319 

101761 

32461759 

17.8606 

6.8328 

2.50379 

3.13480 

1002.2 

79922.9 

320 

102400 

32768000 

17.8885 

6.8399 

2.50515 

3.12500 

1005.3 

80424.8 

321 

103041 

33076161 

17.9165 

6.8470 

2.50651 

3.11527 

1008.5 

80928.2 

322 

103684 

33386248 

17.9444 

6.8541 

2.50786 

3.10559 

1011.6 

81433.2 

323 

104329 

33698267 

17.9722 

6.8612 

2.50920 

3.0959b 

1014.7 

81939.8 

324 

104976 

34012224 

18.0000 

6.8633 

2.51055 

3.08642 

1017.9 

82448.0 

325 

105625 

34328125 

18.0278 

6.8753 

2.51188 

3.07692 

1021.0 

82957.7 

326 

106276 

34645976 

18.0555 

6.8824 

2.51322 

3.06749 

1024.2 

83469.0     I 

327 

106929 

34965783 

18.0831 

6.8894 

2.51455 

3.05810 

1027.3 

83981.8     1 

328 

107584 

35287552 

18.1108 

6.8964 

2.51587 

3.04878 

1030.4 

84496.3     1 

329 

108241 

35611289 

18.1384 

6.9034 

2.51720 

3.03951 

1033.6 

85012.3     1 

330 

108900 

35937000 

18.1659 

6.9104 

2.51851 

3.03030 

1036.7 

85529.9     1 

331 

109501 

36264691 

18.1934 

6.9174 

2.51983 

3.02115 

1039.9 

86049.0     1 

332 

110224 

36594368 

18.2209 

6.9244 

2.52114 

3.01205 

1043.0 

86569.7     1 

333 

110889 

36926037 

18.2483 

6.9313 

2.52244 

3.00300 

1046.2 

87092.0     1 

334 

111556 

37259704 

18.2757 

6.9382 

2.52375 

2.99401 

1049.3 

87615.9     1 

335 

112225 

37595375 

18.3030 

6.9451 

2.52504 

2.98507 

1052.4 

88141.3     1 

336 

112896 

37933056 

18.3303 

6.9521 

2.52634 

2.  976  19 

1055  6 

88668.3     1 

337 

113569 

38272753 

18.3576 

6.95S9 

2.52763 

2.96736 

1058.7 

89196.9     1 

338 

114244 

386144721 

18.3848 

(>.%5S 

2.52892 

2.95858 

1061.9 

89727.0     1 

339 

114921 

38958219 

18.4120 

6.9727 

2.53020 

2.94985 

1065.0 

90258.7     1 

340 

115600 

39304000 

18.4391 

6.9795 

2.53148 

2.94118 

1068.1 

90792.0     1 

341 

116281 

39651821 

18.4662 

6  9864 

2.53275 

8.98255 

1071.3 

91326.9     1 

34* 

116964 

400011)88 

18.4932 

6.9932 

2.53408 

2!92308 

1074.4 

91863.3     1 

343 

117649 

40453607 

18.5203 

7.0000 

2.53529 

2.91545 

1077.6 

92401.3     1 

344 

118336 

40707584 

18.5472 

7.0068 

2.53656 

2.90698 

1080.7 

92940.9     I 

345 

119025 

41063625 

18.5742 

7.0136 

2.53782 

2.89855 

1083.8 

93482.0 

346 

119716 

41421736 

18.6011 

7.0203 

2.53908 

2.89017 

1087.0 

94024.7 

347 

120409 

41781923 

18.6279 

7.0271 

2.54033 

2.88184 

1090.1 

94569.0 

348 

121104 

42111192 

18.6548 

7.0338 

2.54158 

2.87356 

1093.3 

95114.9 

349 

121801 

42508549 

18.6815 

7.0406 

2.54283 

2.86533 

1096.4 

95662.3 

350 

122500 

42875000 

18.7083 

7.0473 

2.54407 

2.85714 

1099.6 

96211.3 

351 

123201 

43243551 

18.7350 

7.0540 

2.54531 

2.84900 

1102.7 

96761.8 

352 

123904 

43614208 

18.7617 

7.0607 

2.54654 

2.84091 

1105.8 

97314.0 

353 

124609 

43986977 

18.7883 

7.0674 

2.54777 

2.83286 

1109.0 

97867.7 

354 

125316 

44361864 

18.8149 

7.0740 

2.54900 

2.82486 

1112.1 

98423.0 

355 

126025 

44738875 

18.8414 

7.0807 

2.55023 

2.81690 

1115.3 

98979.8 

356 

126736 

45118016 

18.8680 

7.0873 

2  55145 

2.80899 

1118.4 

99538.2 

357 

127449 

45499293 

18.8944 

7.0940 

2.55267 

2.80112 

1121.5 

100098 

358 

128164 

45882712 

18.9209 

7.1006 

2.65388 

2.79330 

1124.7 

100660 

359 

128881 

462(58279 

18.9473 

7.1072 

2.55509 

2.78552 

1127.8 

101223 

, 

NATIONAL  TUBE  COMPANY.                      289 

Squares,  Cubes,  Square  Roots,  Cube  Roots,  Logarithms,  Etc. 

(CONTINUED.) 

No. 

Sq. 

Cube. 

Square 
Root. 

Cube 
Root. 

Log. 

1000 
X 
Recip. 

No    =  Dia. 

Circ'm 

Area. 

360 

129600 

46656000 

18.9737 

7.1138 

2.55630 

2.77778 

1131.0 

101788 

361 

130321 

47045881 

19.0000 

7.1204 

2.55751 

2.77008 

1134.1 

102354 

362 

131044 

47437928 

19.0263 

7.1269 

2.55871 

2.76243 

1137.3 

102922 

.    363 

131769 

47832147 

19.0526 

7.1335 

2.55991 

2.75482 

1140.4 

103491 

364 

132496 

48228544 

19.0788 

7.1400 

2.56110 

2.74725 

1143.5 

104062 

365 

133225 

48627125 

19.1050 

7.1466 

2.56229 

2.73973 

1146.7 

104635 

366 

133956 

49027896 

19.1311 

7.1531 

2.56348 

2.73224 

1149.8 

105209 

367 

134689 

49430863 

19.1572 

7.1596 

2.56467 

2.72480 

1153.0 

105785 

368 

135424 

49836032 

19.1833 

7.1661 

2.56585 

2.71739 

1156.1 

106362 

369 

136161 

50243409 

19.2094 

7.1726 

2.56703 

2.71003 

1159.2 

106941 

370 

136900 

50653000 

19.2354 

7.1791 

2.56820 

2.70270 

1162.4 

107521 

371 

137641 

51064811 

19.2614 

7.1855 

2  56937 

2.69542 

1165.5 

108103 

372 

138334 

51478848 

19.2873 

7.1920 

2.57054 

2.68817 

1168.7 

108687 

373 

139129 

51895117 

19.3132 

7.1984 

2.57171 

2.68097 

1171.8 

109272 

374 

139876 

52313624 

19.3391 

7.2048 

2.57287 

2.67380 

1175.0 

109858 

375 

140625 

52734375 

19.3649 

7.2112 

2.57403 

2.66667 

1178.1 

110447 

376 

141376 

53157376 

19.3907 

7.2177 

2.57519 

2.65957 

1181.2 

111036 

377 

142129 

53582633 

19.4165 

7.2240 

2.57634 

2.65252 

1184.4 

111628 

378 

142884 

54010152 

19.4422 

7.2304 

2.57749 

2.64550 

1187.5 

112221 

379 

143641 

54439939 

19.4679 

7.2368 

2.57864 

2.63852 

1190.7 

112815 

380 

144400 

54872000 

19.4936 

7.2432 

2.57978 

2.63158 

1193.8 

113411 

381 

145161 

55306341 

19.5192 

7.2495 

2.58093 

2.62467 

1196.9 

114009 

382 

145924 

55742968 

19.5448 

7.2558 

2.58206 

2.61780 

1200.1 

114608 

383 

146689 

56181887 

19.5704 

7.2622 

2.58320 

2.61097 

1203.2 

115209 

384 

147456 

56623104 

19.5959 

7.2685 

2.58433 

2.60417 

1206.4 

115812 

385 

148225 

57066625 

19.6214 

7.2748 

2.58546 

2.59740 

1209.5 

116416 

386 

148996 

57512456 

19.6469 

7.2811 

2.58659 

2.59067 

1212.7 

117021 

387 

149769 

57960603 

19.6723 

7.2874 

2.58771 

2.58398 

1215.8 

117628 

388 

150544 

58411072 

19.6977 

7.2936 

2.58883 

2.57732 

1218.9 

118237 

389 

151321 

58863869 

19.7231 

7.2999 

2.58995 

2.57069 

1222.1 

118847 

390 

152100 

59319000 

19.7484 

7.3061 

2.59106 

2.56410 

1225.2 

119459 

391 

152881 

59776471 

19.7737 

7.3124 

2.59218 

2.55755 

1228.4 

120072 

392 

153664 

60236288 

19.7990 

7.3186 

2.59329 

2.55102 

1231.5 

120687 

393 

154449 

60698457 

19.8242 

7.3248 

2.59439 

2.54453 

1234.6 

121304 

394 

155236 

61162984 

19.8494 

7.3310 

2.59550 

2.53807 

1237.8 

121922 

395 

156025 

61629875 

19.8746 

7.3372 

2.59660 

2.53165 

1240.9 

122542 

396 

156816 

62099136 

19.8997 

7.3434 

2.59770 

2.52525 

1244.1 

123163 

397 

157609 

62570773 

19.9249 

7.3496 

2.59879 

2.51889 

1247.2 

123786 

398 

158404 

63044792 

19.9499 

7.3558 

2.59988 

2.51256 

1250.4 

124410 

399 

159201 

63521199 

19.9750 

7.3619 

2.60097 

2.50627 

1253.5 

125036 

400 

160000 

64000000 

20.0000 

7.3681 

2.60206 

2.50000 

1256.6 

125664 

401 

160801 

64481201 

20.0250 

7.3742 

2.60314 

2.49377 

1259.8 

126293 

402 

161604 

64964808 

20.0499 

7.3803 

2.60423 

2.48756 

1262.9 

126923 

403 

162409 

65450827 

20.0749 

7.3864 

2.60531 

2.48139 

1266.1 

127556 

404 

163216 

65939264 

20.0998 

7.3925 

2.60638 

2.47525 

1269.2 

128190 

290                      NATIONAL  TUBE  COMPANY. 

Squares,  Cubes,  Square  Roots,  Cube  Roots,  Logarithms,  Etc.  1 

(CONTINUED.) 

Square 

Cube 

1000 

No.  =  Dia.       1 

No. 

Sq. 

Cube. 

Root. 

Root. 

Log. 

X 
Recip. 

Circ'm 

Area.     1 

405 

164025 

66430125 

20.1246 

7.3986 

2.60746 

2.46914 

1272.3 

128825     1 

406 

164836 

66923416 

20.1494 

7.4047 

2.60853 

2.46305 

1275.5 

129462     1 

407 

165649 

67419143 

20.1742 

7.4108 

2.60959 

2.45700 

1-278.6 

130100     1 

408 

166464 

67917312 

20.1990 

7.4169 

2.61066 

2.45098 

1281.8 

130741     1 

409 

167281 

68417929 

20.2237 

7.4229 

2.61172 

2.44499 

1284  9 

131382     1 

410 

168100 

68921000 

20.2485 

7.4290 

2.61278 

2.43902 

1288.1 

132025     1 

411 

168921 

69426531 

20.2731 

7.4350 

2.61384 

2.43309 

1291.2 

132670     1 

412 

169744 

69934528 

20.2978 

7.4410 

2.61490 

2.42718 

1294.3 

133317     1 

413 

170569 

70444997 

20.3224 

7.4470 

2.61595 

2.42131 

1297.5 

133965     1 

414 

171396 

70957944 

20.3470 

7.4530 

2.61700 

2.41546 

1300.6 

134614     1 

415 

172225 

71473375 

20.3715 

7.4590 

2.61805 

2.40964 

1303.8 

135265     1 

416 

173056 

71991296 

20.3961 

7.4650 

2.61909 

2.40385 

1306.9 

135918     1 

417 

173889 

72511713 

20.4206 

7.4710 

2.62014 

2.39808 

1310.0 

136572     1 

418 

174724 

73034632 

20.4450 

7.4770 

2.62118 

2.39234 

1313.2 

137228     I 

419 

175561 

73560059 

20.4695 

7.4829 

2.62221 

2.38664 

1316.3 

137885     1 

420 

176400 

74088000 

20.4939 

7.4889 

2.62325 

2.38095 

1319.5 

138544     1 

421 

177241 

74618461 

20.5183 

7.4948 

2  62428 

2.37530 

1322.6 

139205     1 

422 

178084 

75151448 

20.5426 

7.5007 

2.62531 

2.36967 

1325.8 

139867      1 

423 

1789*9 

75686967 

20.5670 

7.5067 

2.62634 

2.36407 

1328.9 

140531      1 

424 

179776 

76225024 

20.5913 

7.5126 

2.62737 

2.35849 

1332.0 

141196     1 

425 

180625 

76765625 

20.6155 

7.5185 

2.62839 

2.35294 

1335.2 

141863      1 

426 

181476 

77308776 

20.6398 

7.5244 

2.62941 

2.34742 

1338.3 

142531 

427 

182329 

77854483 

20.6640 

7.5302 

2.63043 

2.34192 

1341.5 

143201      1 

428 

183184 

78402752 

20.6882 

7.5361 

2.63144 

2.33645 

1344.6 

143872      1 

429 

184041 

78953589 

20.7123 

7.5420 

2.63246 

2.33100 

1347.7 

144545      1 

430 

184900 

79507000 

20.7364 

7.5478 

2.63347 

2.32558 

1350.9 

145220      1 

431 

185761 

80062991 

20.7605 

7.5537 

2.63448 

2.32019 

1354.0 

145896      1 

432 

186624 

80621568 

20.7846 

7.5595 

2.63548 

2.31482 

1357.2 

146574      1 

433 

187489 

81182737 

20.8087 

7.5654 

2.63649 

2.30947 

1360.3 

147254      1 

434 

188356 

81746504 

20  8327 

-7.5712 

2.63749 

2.30415 

1363.5 

147934 

435 

189225 

82312875 

20.8567 

7.5770 

2.63849 

2.29885 

1366.6 

148617      1 

436 

190096 

82881856 

20.8806 

7.5828 

2.63949 

2.29358 

1369.7 

149301 

437 

190969 

83453453 

20.9045 

7.5886 

2.64048 

2  28833 

1372.9 

149987      1 

438 

191844 

84027672 

20.9284 

7.5944 

2.64147 

2.28311 

1376.0 

150674      1 

439 

192721 

84604519 

20.9523 

7.6001 

2.64246 

2.27790 

1379.2 

151363 

440 

193600 

85184000 

20.9762 

7.6059 

2.64345 

2.27273 

1382.3 

152053 

441 

194481 

85766121 

21.0000 

7.6117 

2.64444 

2.26757 

1385.4 

152745      1 

442 

195364 

86350888 

21.0238 

7.6174 

2.64542 

2  26244 

1388.6 

153439 

443 

196249 

86938307 

21.0476 

7.6232 

2.64640 

2.25734 

1391.7 

154134 

444 

197136 

87528384 

21.0713 

7.6289 

2.64738'  2.25225 

1394.9 

154830 

j 

445 

198025 

88121125 

21.0950 

7.6346 

2.64836 

2.24719 

1398.0 

155528 

446 

198916 

88716536 

21.1187 

7.6403 

2.649&S 

2.24215 

1401.2 

156228 

447 

199809 

89314623 

21.1424 

7.6460 

2.65031 

2.23714 

1404.3 

156930 

448 

200704 

89915392 

21.1660 

7.6517 

2.65128 

2.23214 

1407.4 

157633 

449 

2016011  90518849 

21.1896 

7.6574 

2.65225 

2.22717 

1410.6 

158337 

NATIONAL  TUBE  COMPANY.                     291 

Squares,  Cubes,  Square  Roots,  Cube  Roots,  Logarithms,  Etc. 

(CONTINUED.) 

No. 

450 
451 
452 
453 
454 

Sq. 

Cube. 

Square 
Root. 

Cube 
Root. 

Log. 

1000 
X 
Recip. 

No.  =  Dia. 

Circ'm 

Area. 

202500 
20:3401 
204304 
205209 
206116 

91125000 
91733851 
92345408 
92959677 
93576664 

21.2132 
21.2368 
21.2603 
21.2838 
21.3073 

7.6631 
7.6688 
7.6744 
7.6801 
7.6857 

2.65321 
2.65418 
2.65514 
2.65610 
2.65706 

2.22222 

2.21730 
2.21239 
2.20751 
2.20264 

1413.7 
1416.9 
1420.0 
1423.1 
1426.3 

159043 
159751 
160460 
161171 
161883 

455 
456 
457 

458 
459 

207025 

207936 
208849 
209764 
210681 

94196375 
94818816 
95443993 
96071912 
96702579 

21.3307 
21.3542 
21.3776 
21  .4009 
21.4243 

7.6914 
7.6970 

7.7026 
7.7082 
7.7138 

2.65801 
2.65896 
2.05992 
2  66087 
2.66181 

2.19780 
2.19298 
2.18818 
2.18341 
2.17865 

1429.4 
1432.6 
1435.7 
1438.9 
1442.0 

162597 
163313 
164030 
164748 
165468 

460 
461 
462 
463 
464 

211600 
212521 
213444 
214369 
215296 

97:536000 
97972181 
98611128 
99252847 
99897344 

21.4476 
21  .4709 
21.4942 
21.5174 
21.5407 

7.7194 
7.7250 
7.7306 
7.7362 

7.7418 

2.66276 
2.66370 
2.66464 
2.66558 
2.66652 

2.17391 
2.16920 
2.16450 
2.15983 
2.15517 

1445.1 
1448.3 
1451.4 
1454.6 
1457.7 

166190 
166914 
167639 
168365 
169093 

465 
466 
467 
468 
469 

216225 
217156 
218089 
219024 
219961 

100544625 
101194696 
101847563 
102503232 
103161709 

21.5639 
21.5870 
21.6102 
21.6-333 
21.6564 

7.7473 
7.7529 
7.7584 
7.7639 
7.7695 

2.66745 
2.66839 
2.66932 
2.67025 
2.67117 

2.15054 
2.14592 
2.141:33 
2.13675 
2.13220 

1460.8 
1464.0 
1467.1 
1470.3 
1473.4 

169823 
170554 
171287 
172021 
172757 

470 
471 
472 

473 

474 

220900 
221841 

•.'2-j;st 

223729 
224676 

103823000 
104487111 
105154048 
105823817 
106496424 

21.6795 
21.7025 

21.7256 
21.7486 
21.7715 

7.7750 
7.7805 
7.7860 
7.7915 
7.7970 

2.67210 
2.67302 
2.67394 
2.67486 
2.67578 

2.12766 
2.12314 
2.11864 
2.11417 
2.10971 

1476.5 
1479.7 
1482.8 
1486.0 
1489.1 

173494 
174234 
174974 
175716 
176460 

475 
476 

477 
478 
479 

225625 
226576 
227529 
228484 
229441 

107171875 
107850176 
1085313:33 
109215352 
109902239 

21.7945 
21.8174 
21  .8403 
21.8632 
21.8861 

7.8025 
7.8079 
7.8134 
7.8188 
7.8243 

2.67669 
2.67761 
2.67852 
2.67943 
2.68034 

2.10526 
2.10084 
2.09644 
2.09205 
2.08768 

1492.3 
1495.4 
1498.5 
1501.7 
1504.8 

177205 
177952 
178701 
179451 
180203 

480 
481 

482 
483 

484 

230400 
231361 
2:«:5:J  J 
233289 
234256 

110592000 
111284641 
111980168 
112678587 
113379904 

21.9089 
21.9317 
21  .9545 
21.9773 
22.0000 

7.8297 
7.8352 
7.8406 
7.8460 
7.8514 

2.68124 
2.68215 
2.68305 
2.68395 
2.68485 

2.08333 
2.07900 
2.07469 
2.07039 
2.06612 

1508.0 
1511.1 
1514.3 
1517.4 
1520.5 

180956 
181711 
182467 
183225 
183984 

1485 
486 
487 
488 
489 

235225 
236196 
237169 
238144 
239121 

114084125 
114791256 
115501303 
116214272 
116930169 

22.0227 
22.0454 
22.0681 
22.0907 
22.1133 

7.8568 
7.8622 
7.8676 
7  8730 
7.8784 

2.68574 
2.68664 
2  68753 
2.68842 
2.68931 

2.06186 
2.05761 
2.05339 
2.04918 
2.04499 

1523.7 
1526.8 
1530.0 

isas.i 

1536.2 

184745 
185508 
186272 
187038 
187805 

490 
491 
492 
493 
494 

240100 
241081 
242064 
243049 
244036 

117649000 
118370771 
119095488 
119823157 
120553784 

22.U359 
22.1585 
22.1811 
22.2036 
22.2261 

7.8837 
7.8891 
7.8944 
7.8998 
7.9051 

2.69020 
2.69108 
2.69197 
2.69285 
2.69373 

2.04082 
2.03666 
2.03252 
2.02840 
2  02429 

1539.4 
1542.5 
1545.7 
1548.8 
1551.9 

188574 
189345 
190117 
190890 
191665 

. 

292                     NATIONAL  TUBE  COMPANY. 

Squares,  Cubes,  Square  Roots,  Cube  Roots,  Logarithms,  Etc* 

(CONTINUED.) 

No. 

Sq. 

Cube. 

Square 
Root. 

Cube 
Root. 

Log. 

1000 
X 
Recip. 

No.  =  Dia. 

Circ'm 

Area. 

495 

245025 

121287375 

22.2486 

7.9105 

2.69461 

2.02020 

1555.1 

192442 

496 

246016 

122023936 

22.2711 

7.9158 

2.69548 

2.01613 

1558.2 

193221 

497 

247009 

122763473 

22.2935 

7.9211 

2.69636 

2.01207 

1561.4 

194000 

498 

248004 

123505992 

22.3159 

7.9264 

2.69723 

2.00803 

1564.5 

194782 

499 

249001 

124251499 

22.3383 

7.9317 

2.69810 

2.00401 

1567.7 

195565 

500 

250000 

125000000 

22.3607 

7.9370 

2.69897 

2.00000 

1570.8 

196350 

501 

251001 

125751501 

22.3830 

7.9423 

2.69984 

1.99601 

1573.9 

197136 

502 

252004 

126506008 

22.4054 

7.9476 

2.70070 

1.99203 

1577.1 

197923 

503 

253009 

127263527 

22.4277 

7.9528 

2.70157 

1.98807 

1580.2 

198713 

504 

254016 

128024064 

82.4499 

7.9581 

2.70243 

1.98413 

1583.4 

199504 

505 

255025 

128787625 

22.4722 

7.9634 

2.70329 

1.98020 

1586.5 

200296 

506 

256036 

129554216 

22.4944 

7.9686 

2.70415 

1.97629 

1589.7 

201090 

507 

257049 

130323843 

22.5167 

7.9739 

2.70501 

1.97239 

1592.8 

201886 

508 

258064 

131096512 

22.5389 

7.9791 

2.70586 

1.96850 

1595.9 

202683 

509 

259081 

131872229 

22.5610 

7.9843 

2.70672 

1.96464 

1599.1 

203482 

510 

260100 

132651000 

22.5832 

7.9896 

2.70757 

1.96078 

1602.2 

204282 

511 

261121 

133432831 

22.6053 

7.9948 

2.70842 

1.95695 

1605.4 

205084 

512 

262144 

134217728 

22.6274 

8.0000 

2.70927 

1.95312 

1608.5 

205887 

513 

263169 

135005697 

22.6495 

8.0052 

2.71012 

1.94932 

1611.6 

206692 

514 

264196 

135796744 

22.6716 

8.0104 

2.71096 

1.94553 

1614.8 

207499 

515 

265225 

136590875 

22.6936 

8.0156 

2.71181 

1.94175 

1617.9 

208307 

516 

266256 

137388096 

22.7156 

8.0208 

2.71265 

1.93798 

1621.1 

209117 

517 

267289 

138188413 

22.7376 

8.0260 

2.71349 

1.93424 

1624.2 

209928 

518 

268324 

138991832 

22.7596 

8.0311 

2.71433 

1.93050 

1627.3 

210741 

519 

269361 

139798359 

22.7816 

8.0363 

2.71517 

1.92678 

1630.5 

211556 

520 

270400 

140608000 

22.8035 

8.0415 

2.71600 

1  92308 

1633.6 

212372 

521 

271441 

141420761 

22.8254 

8.0466 

2.71684 

1.91939 

1636.8 

213189 

522 

272484 

142236648 

22.8473 

8  0517 

2.71767 

1  91571 

1639.9 

214G08 

523 

273529 

143055667 

22.8692 

8.0569 

2.71850 

1.91205 

1643.1 

214829 

524 

274576 

143877824 

22.8910 

8.0620 

2.71933 

1.90840 

1646.2 

215651 

525 

275625 

144703125 

22.9129 

8.0671 

2.72016 

1.90476 

1649.3 

216475 

526 

276676 

145531576 

22.9347 

8.0723 

2.72099 

1.90114 

1652.5 

217301 

527 

27773 

146363183 

22.9565 

8.0774 

2.72181 

1.89753 

1655.6 

218128 

528 

278784 

147197952 

22.9783 

8.0825 

2.72263 

l.S!«91 

1658.8 

218956 

529 

279841 

148035889 

23.0000 

8.0876 

2.72346 

1.89036 

1661.9 

219787 

530 

280900 

148877000 

23.0217 

8.0927 

2.72428 

1.88679 

1665.0 

220618 

531 

281961 

149721291 

23.0434 

8.0978 

2.72509 

1.88324 

1668.2 

221452 

532 

28302- 

150568768 

23.0651 

8.1028 

2.72591 

1.87970 

1671.3 

222287 

533 

-  'Sins'. 

151419427 

23.0868 

8.1079 

2.72673 

1.87617 

1674.5 

223123 

534 

285156 

152273304 

23.1084 

8.1130 

2.72754 

1.87266 

1677.6 

223961 

535 

286225 

158130875 

23.1301 

8.1180 

2.72835 

1.86916 

1680.8 

224801 

536 

28725M 

153990656 

23.1517 

8.1231 

2.7291C 

1.86567 

1683.9 

225642 

537 

888861 

154854153 

23.1733 

8.1281 

2.72W; 

l.«C)22( 

1687.0 

226484 

538 

28944 

155720872 

23.1948 

8.1332 

2.73078 

1.85874 

1690.2 

227329 

539 

390521 

156590819 

23.2164 

8.1382 

2.73159 

1.85529 

1693.3 

228175 

NATIONAL  TUBE  COMPANY.                      293 

Squares,  Cubes,  Square  Roots,  Cube  Roots,  Logarithms,  Etc. 

(CONTINUED.) 

No. 

540 
541 
542 
543 
544 

Sq. 

Cube. 

Square 
Root. 

Cube 
Root. 

Log. 

1000 
X 
Recip. 

No.  =  Dia. 

Circ'm 

Area. 

291600 
292681 
293764 
894849 
295936 

157464000 
158340421 
159220088 
160103007 
160989184 

23.2379 
23.2594 
23.2809 
23.3024 
23.3238 

8.1433 
8.1483 
8.1533 
8.1583 
8.1633 

2  73239 
2.73320 
2.73400 
2.73480 
2.73560 

1.85185 
1.84843 
1.84502 
1.84162 
1.83824 

1696.5 
1699.6 
1702.7 
1705.9 
1709.0 

229022 
229871 
230722 
231574 
232428 

545 
546 
547 
548 
549 

297025 

5>(.»S11li 
299209 
300304 
301401 

161878625 
162771336 
1  63667323 
164566592 
165469149 

23.3452 
23.3666 
23.3880 
23.4094 
23.4307 

8.1683 
8.1733 

8.1783 
8.1833 
8.1882 

2.73640 
2.73719 
2.73799 
1-73878 
2.73957 

1.83486 
1.83150 
1.82815 
1.82482 
1.82149 

1712.2 
1715.3 
1718.5 
1721.6 
1724.7 

233283 
234140 
234998 
235858 
236720 

550 
551 
552 
553 
554 

302500 
303601 
304704 
305809 
306916 

166375000 
167284151 
168196608 
169112377 
170031464 

23.4521 
23.4734 
23.4947 
23.5160 
23.5372 

8.1932 
8.1982 
8.2031 
8.2081 
8.2130 

2.74036 
2.74115 
2.74194 
2.74273 
2.74351 

1.81818 
1.81488 
1.81159 
1.80832 
1.80505 

1727.9 
1731.0 
1734.2 
1737.3 
1740.4 

237583 
238448 
239314 
240182 
241051 

555 

556 
557 
558 
559 

30S025 
309136 
310249 
311364 
312481 

170953875 
171879616 
172808693 
173741112 
174676879 

23.5584 
23.5797 
23.6008 
23.6220 
23.6432 

8.2180 
8.2229 

8.2278 
8.2327 
8.2377 

2.74429 
2.74507 

2.74586 
2  74663 
2.74741 

1.80180 
1.79856 
1.79533 
1.79211 
1.78891 

1743.6 
1746.7 
1749.9 
1753.0 
1756.2 

241922 
242795 
243669 
244545 
245422 

560 
561 
562 
563 
564 

313600 
314721 
315844 

316969 
318096 

175616000 
176558481 
177504328 
178453547 
179406144 

23  6643 
23.6854 
23.7065 
23.7276 

23.7487 

8.2426 
8.2475 
8.2524 
8.2573 
8.2621 

2.74819 
2.74896 
2.74974 
2.75051 
2.75128 

1.78571 
1.78253 
1.77936 
1.77620 
1.77305 

1759.3 
1762.4 
1765.6 
1768.7 
1771.9 

246301 
247181 
248063 
248947 
249832 

565 
566 
567 
568 
569 

319225 
320356 

321489 
:;-J-.v,-j| 
323761 

180362125 
181321496 
182284263 
183250432 
184220009 

23.7697 
23.7908 
23.8118 
23.8328 
23.8537 

8.2670 
8.2719 
8.2768 
8.2816 
8.2865 

2.75205 
2.75282 
2.75358 
2.75435 
2.75511 

1.76991 
1.76678 
1.76367 
1.76056 
1.75747 

1775.0 
1778.1 
1781.3 
1784.4 
1787.6 

250719 
251607 
252497 
253388 
254281 

570 
571 
572 
573 
574 

324900 
326041 
327184 

:;•>:;•.". 
329476 

185193000 
186169411 
187149248 
188132517 
189119224 

23.8747 
23.8956 
23.9165 
23.9374 
23.9583 

8.2913 
8.2962 
8.3010 
8.3059 
8.3107 

2.75587 
2.75664 
2.75740 
2.75815 
2.75891 

1.75439 
1.75131 
1.74825 
1.74520 
1.74216 

1790.7 
1793.5 
1797.0 
1800.1 
1803.3 

255176 
256072 
256970 
257869 
258770 

575 
576 
577 

578 
579 

330625 
331776 
332929 
334084 
335241 

190109375 
191102976 
192100033 
193100552 
194104539 

23.9792 
24.0000 
24.0208 
24.0416 
24.0624 

8.3155 
8.3203 
8.3251 
8.3300 
8.3348 

2.75967 
2.76042 
2.76118 
2.76193 
2.76268 

1.73913 
1.73611 
1.73310 
1.73010 
1.72712 

1806.4 
1809.6 
1812.7 
1815.8 
1819.0 

259672 
260576 
261482 
262389 
263298 

580 

581 

583 
584 

336400 
337561 
338724 
339889 
341056 

195112000 
196122941 
197137368 
198155287 
199176704 

24.0832 
24.1039 
24.1247 
24.1454 
24.1661 

8.3396 
8.3443 
8.3491 
8.3539 

8.3587 

2.76343 
2.76418 
2.76492 
2.76567 
2.76641 

1.72414 
1.72117 
1.71821 
1.71527 
1.71233 

1822.1 
1825.3 
1828.4 
1831.6 
1834.7 

264208 
265120 
266033 
266948 
267865 

i  , 

294                      NATIONAL  TUBE  COMPANY. 

Squares,  Cubes,  Square  Roots,  Cube  Roots,  Logarithms,  Etc. 

(CONTINUED.) 

No. 

Sq. 

Cube. 

Square 
Root. 

Cube 
Root. 

Log. 

1000 
X 
Recip. 

No.  =  Dia. 

Circ'm 

Area. 

585 

342225 

200201625 

24.1868 

8.3634 

2.76716 

1.70940 

1837.8 

268783 

586 

848896 

201230056 

24.2074 

8.3682 

2.76790 

1.70649 

1841.0 

269701 

587 

344569 

21  2262003 

24.2281 

8.3730 

2.76864 

1.70358 

1844.1 

270624 

588 

345744 

203297472 

24.2487 

8.3777 

2.76938 

1.70068 

1847.3 

271547 

589 

346921 

204336469 

24.2693 

8.3825 

2.77012 

1.69779 

1850.4 

272471 

590 

348100 

205379000 

24.2899 

8.3872 

2.77085 

1.69492 

1853.5 

273397 

591 

349281 

206425071 

24.3105 

8.3919 

2.77159 

1.69205 

1856.7 

274325 

592 

3.50  J  64 

207474688 

24.3311 

8.3967 

•)  77->:!-> 

1.68919 

1859.8 

275254 

593 

351649 

208527857 

24.3516 

8.4014 

2.  77305 

1.68634 

1863.0 

276184 

594 

352836 

209584584 

24.3721 

8.4061 

2.77379 

1.68350 

1866.1 

277117 

595 

354025 

210644875 

24.3926 

8.4108 

2.77452 

1.68067 

1869.3 

278051 

596 

355216 

211708736 

24.4131 

8.4155 

2.77525 

1.67785 

1872.4 

278986 

597 

356409 

212776173 

24.4336 

8.4202 

2.77597 

1.67504 

1875.5 

279923 

598 

357604 

213847192 

24.4540 

8.4249 

2.77670 

1.67224 

1878.7 

280862 

599 

358801 

214921799 

24.4745 

8.4296 

2.77743 

1.66945 

1881.8 

281802 

600 

3600T>0 

216000000 

24.4949 

8.4343 

2.77815 

1.66667 

1885.0 

282743 

601 

361201 

217081801 

24.5153 

8.4390 

2.77887 

1.66389 

1888.1 

283687 

602 

362404 

218167208 

24.5:357 

8.4437 

2.77960 

1.66113 

1891.2 

284631 

603 

363609 

219256227 

24.5561 

8.4484 

2.78032 

1.65837 

1894.4 

285578 

604 

364816 

220348864 

24.5764 

8.4530 

2.78104 

1.65563 

1897.5 

286526 

605 

366025 

221445125 

24.5967 

8.4577 

2.78176 

1.65289 

1900.7 

287475 

606 

367236 

222.545016 

24.6171 

8.4623 

2.78247 

1.65017 

1903.8 

288426 

607 

368449 

223648543 

24  6374 

8.4670 

2.78319 

1.64745 

1907.0 

289379 

608 

369664 

224755712 

24.6577 

8.4716 

2.78390 

1.64474 

1910.1 

290333 

609 

370881 

225866529 

24.6779 

8.4763 

2.78462 

1.64204 

1913.2 

291289 

610 

372100 

226981000 

24.6982 

8.4809 

2.78533 

1.63934 

1916.4 

292247 

611 

873881 

228099131 

24.7184 

8.4856 

2.78604 

1.63666 

1919.5 

293206 

612 

374544 

229220928 

24.7386 

8.4902 

2.78675 

1.63399 

1922.7 

294166 

613 

375769 

230346397 

24.7588 

8.4948 

2.78746 

1.63132 

295128 

614 

376996 

231475544 

24.7790 

8.4994 

2.78817 

1.62866 

I928/J 

296092 

615 

378225 

232608375 

24.7992 

8.5040 

2.78888 

1.62602 

1932.1 

297057 

616 

2:33744896 

24.8193 

S.50S6 

2.78958 

1.1W33K 

298024 

617 

880680 

234885113 

24.8395 

8  5132 

2.79029 

1.62075 

193814 

298992 

618 

381924 

236029032 

24.8596 

8.5178 

2.79099 

1.61812 

1941.5 

299962 

619 

383161 

237176659 

24.8797 

8.5224 

2.79169 

1.61551 

1944.7 

300934 

620 

384400 

238328000 

24.8998 

8.5270 

2.79239 

1.61290 

1947.8 

301907 

621 

385641 

239483061 

24.9199 

8.5316 

2.79309 

1.61031 

1950.9 

302882 

622 

386884 

240641848 

24.9399 

8.5362 

2.79379 

1.60772 

1954.1 

303858 

623 

388129 

241804367 

24.9600 

8.5408 

2.79449 

1.60514 

1957.2 

304836 

624 

389376 

242970624 

24.9800 

8.5453 

2.79518 

1.60256 

1960.4 

305815 

625 

390625 

244140625 

25.0000 

8.5499 

2.79588 

1.60000 

1963.5 

306796 

626 

391876 

245314376 

25.0200 

8.5544 

2.79657 

1.59744 

1966.6 

307779 

627 

393129 

246491883 

25.0400 

8.5590 

2.79727 

1.59490 

1969.8 

308763 

628 

394384 

247673152 

25.0599 

8.5635 

2.79796 

1.59236 

1972.9 

309748 

629 

868641 

248858189 

25.0799 

8.5681 

2.79865 

1.58983 

1976.1 

310736 

NATIONAL  TUBE  COMPANY.                      295 

Squares,  Cubes,  Square  Roots,  Cube  Roots,  Logarithms,  Etc. 

(CONTINUED.) 

No. 

Sq. 

Cube. 

Square 
Root. 

Cube 
Root. 

Log. 

1000 
X 
Recip. 

No.  =  Dia. 

Circ'm 

Area. 

630 

396900 

250047000 

25.0998 

8.5726 

2.79934 

1.58730 

1979.2 

311725 

631 

398161 

251239591 

25.1197 

8.5772 

2.80003 

1.58479 

1982.4 

312715 

632 

399424 

252435968 

25.1396 

8.5817 

2.80072 

1.58228 

1985.5 

313707 

633 

400689 

253636137 

25.1595 

8.5862 

2.8ul40 

1.57978 

1988.6 

314700 

634 

401956    254840104 

25.1794 

8.5907 

2.80209 

1.57729 

1991.8 

315696 

635 

4032251  256047875 

25.1992 

8  5952 

2.80277 

1.57480 

1994  9 

316692 

636 

404496 

257259456 

25.2190 

8.5997 

2.80346 

1.57233 

1998.1 

317690 

637 

405769 

258474853 

25.2389 

8.6043 

2.80414 

1.56986 

2001.2 

318690 

638 

407044 

259694072 

25.2587 

8.6088 

2.80482 

1.56740 

2004.3 

319692 

639 

408321 

260917119 

25.2784 

8.6132 

2.80550 

1.56495 

2007.5 

320695 

640 

409600 

262144000 

25.2982 

8.6177 

2.80618 

1.56250 

2010.6 

321699 

641 

410881 

263374721 

25.3180 

8.6222 

2  80686 

1.56006 

2013.8 

322705 

642 

412164 

264609288 

25.3377 

8.6267 

2.80754 

1.55763 

2016.9 

323713 

643 

41:3449 

.265847707 

25.3574 

8.6312 

2.80821 

1.55521 

2020.0 

324722 

644 

414736 

267089984 

25.3772 

8.6357 

2.80889 

1.55280 

2023.2 

325733 

645 

416025 

268336125 

25.3969 

8.6401 

2.80956 

1.55039 

2026.3 

326745 

646 

417316 

269586136 

25.4165 

8.6446 

2.81023 

1.54799 

2029.5 

327759 

647 

418609 

270840023 

25.4362)  8.6490 

2.81090 

1.54560 

2032.6 

328775 

648 

419904 

272097792 

25.4558 

8.6535 

2.81158 

1.54321 

2035.8 

329792 

649 

421201 

273359449 

25.4755 

8.6579 

2.81224 

1.54083 

2038.9 

330810 

650 

422500 

274625000 

25.4951 

8.6624 

2.81291 

1.53846 

2042.0 

a31831 

651 

423801 

275894451 

25.5147 

8.6668 

2.81358 

1.53610 

2045.2 

332853 

'•      652 

425104 

277167808 

25.5343 

8.6713 

2.81425 

1.53374 

2048.3 

333876 

653 

426409 

278445077 

25.5539 

8.6757 

2.81491 

1.53139 

2051.5 

334901 

|      654 

427716 

279726264 

25.5734 

8.6801 

2.81558 

1.52905 

2054.6 

335927 

655 

429025 

281011375 

25.5930 

8.6845 

2.81624 

1.52672 

2057.7 

a36955 

i      656 

430336 

282300416 

25.6125 

8.6890 

2.81690 

1.52439 

2060  9 

337985 

I      757 

431649 

283593393 

25  6320 

8.6934 

2.81757 

1.52207 

2064.0 

339016 

758 

432964 

284890312 

25.6515 

8.6978 

2.81823 

1.51976 

2067.2 

340049 

659 

434281 

286191179 

25.6710 

8.7022 

2.81889 

1.51745 

2070.3 

341084 

660 

435600 

287496000 

25.6905 

8.7066 

2.81954 

1.51515 

2073.5 

342119 

661 

436921 

288804781 

25.7099 

8.7110 

2.82020 

1.51286 

2076.6 

343157 

662 

438244 

290117528 

25  7294 

8.7154 

2.82086 

1.51057 

!2079.7 

344196 

i      663 

439569 

291434247 

25.7488 

8.7198 

2.82151 

1.50830 

2082.9 

345237 

664 

440896 

292754944 

25.7682 

8.7241 

2.82217 

1.50602 

2086.0 

346279 

665 

442225 

294079625 

25.7876 

8.7285 

2.82282 

1.50376 

2089.2 

347323 

666 

148660 

295408296 

25.8070 

8.7329 

2.82347 

1.50150 

2092.3 

348368 

667 

444889 

296740963 

25.8263 

8.7373 

2.82413 

1.49925 

2095.4 

349415 

668 

446224 

298077632 

25.8457 

8.7416 

2.82478 

1.49701 

2098.6 

350464 

669 

447561 

299418309 

25.8650 

8.7460 

2.82543 

1.49477 

2101.7 

351514 

670 

448900 

300763000 

25.8844 

8.7503 

2.82607 

1.49254 

2104.9 

352565 

671 

450241 

302111711 

25.9037 

8.7547 

2.82672 

1.49031 

2108.0 

353618 

672 

451584 

303464448 

25.9230 

8.7590 

2.82737 

1.48810 

2111.2 

354673 

673 

452929 

304821217 

25.9422 

8.7634 

2.82802 

1.48588 

2114.3 

355730 

674 

454276 

306182024 

25.9615 

8.7677 

2.82866 

1.48368 

2117.4 

356788 

QL.      .,  * 

296                       NATIONAL  TUBE  COMPANY. 

Squares,  Cubes,  Square  Roots,  Cube  Roots,  Logarithms,  Etc. 

(CONTINUED.) 

Square 

Cube 

1000 

No.  =  Dia. 

No. 

Sq. 

Cube. 

Root. 

Root. 

Log. 

X 
Recip 

Circ'm 

Area. 

675 

455625 

307546875 

25.9808 

8.7721 

2.82930 

1.48148 

2120.6 

357847 

676 

456976 

308915776 

26.0000 

8.77(54 

2.8299: 

1.47929 

2123.7 

358908 

677 

158:  129 

310288733 

26.0192 

8.7H07 

2.83055) 

1.47711 

2126.! 

359971 

678 

159681 

311665752 

26.C384 

8.7850 

2.83123 

1.47493 

2130.0 

361035 

679 

461041 

313046839 

26.0576 

8.7893 

2.83187 

1.47275 

2133.1 

362101 

680 

462400 

314432000 

26.0768 

8.7937 

2.83251 

1.47059 

2136.3 

363168 

681 

4(53761 

315821241 

26.09(50 

8.798C 

2.83315 

1.46843 

2139.4 

364237 

682 

465124 

317214568 

26.1151 

8.802: 

2.83378 

1.46628 

2142.6 

365308 

683 

166189 

318611987 

26.1343 

8.  SOW 

2.8314;, 

1.46413 

2145.7 

366380 

684 

467856 

320013504 

26.1534 

8.8109 

2.83506 

1.46199 

2148.9 

367453 

685 

469225 

321419125 

26.1725 

8.8152 

2.83569 

1.45985 

2152.0 

368528 

686 

170.7.16 

322828856 

26.15)16 

8.8194 

2.83632 

1.45773 

2155.1 

369605 

687 

471969 

324242703 

26.2107 

8.8237 

2.8:>,09I 

1.45560 

2158.3 

370684 

688 

47*144 

325660672 

26.2298 

8.8280 

2.83759 

1.45349 

2161.4 

371764 

689 

474721 

327082769 

26.2488 

8.8323 

2.83822 

1.45138 

2164.6 

372845 

690 

476100 

328509000 

26.2679 

8.8366 

2.83885 

1.44928 

2167.7 

373928 

691 

477481 

325)939371 

2(5.28(59 

8.8408 

2.83948 

1.44718 

2170.8 

375013 

692 

478864 

331373888 

26.3059 

8.8451 

2  84011 

1.44509 

2174.0 

376099 

693 

480249 

33281255'! 

26.3249 

8.8493 

2.84073 

1.44300 

2177.1 

377187 

694 

481636 

334255384 

26.3439 

8.8536 

2.84136 

1.44092 

2180.3 

378276 

695 

483025 

335702375 

26.3629 

8.8578 

2.84198 

1.43885 

2183.4 

379367 

696 

484416 

337153536 

26.3818 

8.8621 

2.84261 

1.43678 

2186.6 

380459 

697 

485809 

338(508873 

26.4008 

8.8663 

2.84323 

1.43472 

2189.7 

381554 

698 

487204 

340068392 

26.4197 

8.8706 

2.84386 

1  .  43267 

2192.8 

382649 

699 

488601 

341632099 

26.4386 

8.8748 

2.84448 

1.43062 

2196.0 

383746 

700 

490000 

343000000 

26.4575 

8.8790 

2.84510 

1.42857 

2199.1 

385845 

701 

491401    344472101 

26.4764 

8.8833 

2.84572 

1.42653 

2202.3 

385945 

702 

4928041  34594840H 

26.4953 

8.K875 

2.84634 

1.42450 

2205.4 

387047 

703 

494205) 

847426927 

26.5141 

8  8917 

2.81696 

1.42248 

2208.5 

388151 

704 

495616 

348913664 

26.5330 

8.8959 

2.84757 

1.42046 

2211.7 

389256 

705 

497025 

350402625 

26.5518 

8.9001 

2  84819 

1.41844 

2214.8 

390363 

706 

1981;  ill 

35185)581(5 

26.5707 

8.5)043 

2.H4H80 

1.41(543 

2218.0 

391471 

707 

499849 

853893243 

2(5.5895 

8  9085 

2.81912 

1.41443 

2221.1 

392580 

708 

501264 

354894912 

26.6083 

H.9127 

2.85003 

1.41243 

2221.:} 

35)3692 

709 

502681 

356400829 

26.6271 

8.9169 

2.85065 

1.41044 

2227.4 

394805 

710 

504100 

357911000 

26  6458 

8.9211 

2.85126 

1.40845 

2230.5 

395919 

711 

505.521 

359425431 

26.6616 

8.925:! 

2.85187 

1.40647 

2233.7 

397035 

712 

506911 

3(50944128 

26.6888 

8.9295 

2.85248 

1.4044!) 

22-'  it;  8 

398153 

713 

506869 

362467097 

26.7021 

8.9337 

2.8530!) 

1.40253 

2240  !o 

399272 

714 

509796 

363994344 

26.7208 

8.5)378 

2.85370 

1.40056 

2243.1 

400393 

715 

511225 

365525875 

26.7395 

8.9420 

2.85431 

1.39860 

2246.2 

401515 

716 

512656 

3(570(5169(5 

26.7582    8.9462 

2.85491 

1..  '59(565 

2249.4 

402639 

717 

514069 

368601813 

26.7769 

8.5150:! 

2.85552 

1.39470 

-.'252.:, 

403765 

718 

515524 

370146232 

26.7955 

8.9545 

2.85612 

1.39276 

2255.7 

404892 

719 

516961 

371694959 

26.8142 

8.9587 

2.85673 

1.39082 

2258.8 

406020 

T 

NATIONAL  TUBE  COMPANY.                      297 

Squares,  Cubes,  Square  Roots,  Cube  Roots,  Logarithms,  Etc. 

(CONTINUED.) 

No. 

720 
721 
722 
723 
724 

Sq 

Cube. 

Square 
Root. 

Cube 
Root. 

Log. 

1000 
X 
Recip. 

No.  =  Dia. 

^irc'm 

Area 

518400 
519841 
521284 

5241  76 

:J7324NXM' 

876867048 
877988067 

379503424 

86.8888 
26.8514 

BftiSBSi 
29.9079 

BiOBTO 

8.9711 
B.9758 

2.85733 
8.85794 

•>.S5S51 
2.S51M4 

2.85974 

l.:^| 

1  '.38313 
1.38122 

2261.9 
8865.1 
8868.8 
8871.4 

2274.5 

407150 
408888 

409416 

410550 
411687 

725 
726 
727 

728 
729 

525625 

521076 

531441 

381078125 

884940589 

3s.5s-JS3.5-J 
387420489 

86.9958 

26.9444 
86.9889 
86.9816 

27.0000 

B.9888 

B.9876 
8.9018 
B.9969 

9.0000 

2.86034 

•j.sr.oai 

2i86918 

2.80273 

1.37931 
1.37741 
1.37552 
1.3:363 
1.37174 

2277.7 
8880.8 

8987!l 

2290.2 

419886 

413965 
416108 

416248 
417393 

7:30 
731 
732 
733 
734 

532900 

5.",43.jl 

587288 

538756 

389017000 

89222816* 

393832837 
395446904 

27.0185 

27.  03;  <  > 
87.0556 
27.0740 
27.0924 

9.0041 

9.0082 

9!  01  64 
9.0205 

2.86332 

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2.86451 
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liWTW 

1.36612 
1.  3642I1 
1.36240 

2293.4 
8896.6 
8889.7 

2302  s 
2305.9 

418539 
419688 

481986 

423138 

735 
736 
737 

738 
739 

540225 

541696 
5431  im 
544«Vt4 
546121 

80M6BB7C 

40081555! 

401947275 

403583419 

27.1109 
27.1293 
27.1477 
87.1668 

27.1846 

9.0246 
9.0887 
9.088B 
9.0888 

9.0410 

2.8»ir,25« 
8.8688B 

8.86747 

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2.86864 

1.36054 
1.85870 
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l!  35318 

2309.1 
2312.2 
2315.4 
2318.5 
2321.6 

424293 

425448 
426604 
427762 
428922 

740 
741 
742 
743 
744 

547600 
549081 
5.50.564 
558041 
553536 

405224000 

410172407 
411830784 

27.2029 
27.2213 
27.23517 
27.2580 
27.2764 

9.0450 
9.0491 
9.0532 
9.0572 
9.0613 

2.86923 

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2.S7W9 
2.87157 

1.35135 
1.34953 
1.34771 
1.34590 
1.34409 

2324.8 
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2334.2 
2337.3 

430084 
431247 
432412 
433578 
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740 
747 
748 
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555025 
5WW16 
558009 
559.504 
561001 

413493625 

415160931 

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27.2947   9.0654 
27.3130   9.0694 
27.3313'  9.0735 
27.3496J  9.0775 
27.3679   9.0816 

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Z'.878M 

2.87448 

1.34228 
1.34048 
1.33865 
1.33690 
1.33511 

2340.5 
8848.6 

2346.8 
2349.9 
2353.1 

435916 
437087 
438259 
439433 
440609 

750 
751 
752 
753 
754 

562500 
564001 
565504 
567009 
568516 

421875000 
423564751 

4  2.52.5'.  Mjus 

428661064 

27.3861    9.0856 
27.4044   9.0896 
27.4226:  9.0937 
27.4408!  9.0977 
27.4591    9.1017 

2.87506 
8.87564 

•J.STti-J-J 
2'.87737 

1.33333 
1.33156 
1.32979 
1.32802 
1.32626 

2356.2 
8899.8 
8868.6 
8865.6 

2368.8 

441786 
442965 
444146 
445328 
446511 

755 
756 
757 
758 
759 

570025 
571681 
578041 

574.561 
576081 

43a368875 
432081  21  » 
188798001 
435515)512 
437245479 

!    9.1057 

27.4H.V,    (.».Kf.is 
27.5136   9.1138 
27.5318   9.1178 
27.5500   9.1218 

8.87796 

2.S7S.5-J 
-J.s7.Ui 

nmS& 

1.32450 
1.32275 
1.32100 
1.31926 
1.31752 

2371.9 
2375.0 
8878.8 
2881.  J 
2384.5 

447697 
448888 
460078 

451262 
452453 

760 
761 
762 
763 

764 

577600 
579121 
580644 
582105 

5S361H 

438976000 
44071108 
442450728 
44419494" 
44.5943744 

27.5681    9.1258 
27.5862;  9.1298 
27.6043    9.1338 
27.6225    H.i:  :',',* 
27.6405    9.1418 

2.88081 

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2.88309 

1.31579 
1.31406 
1.31234 
1.31062 
1.30890 

2387.6 
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8898.9 
8897.1 

2400.2 

453646 
454841 
456037 
457234 
458434 

NATIONAL  TUBE  COMPANY. 


Squares,  Cubes,  Square  Roots,  Cube  Roots,  Logarithms,  Etc* 


(CONTINUED.) 


Sq. 


Cube. 


Square 
Root. 


451217663 

452984832  27.7128 

5913611  454756609  27!7308 

592900  456533000  27.7489 

594441  458:314011:  27.7669 

595984  460099648  27.7849 

597529  461889917  27.8029 

599076,  463684824  27.8209 


600625   465484375 
602176    467288576 


605284  470910952 
606841,  47-2729139 

608400!  474552000 
609961  476379541 
611524  478211768 
613089  480048687 
614656;  481890304 


617796    485587656 
619369    487443403 


622521  491169069 

624100 
085861 
0£74M 


106617897 

500566184 

502459875 
5048688M 

506261573 
508169592 
510082399 

640000J  512000000 
513922401 


519718464   28.3549 


28.3725 
523608616   28.3901 
28.4077 


27.8747 
27.8927 
27.9106 

27.9285 
27.9464 
27.9643 


28.0179 
28,0357 
28.0535 
28.0713 


28.1247 

28.1425 
28.1603 
28.1780 

28.1957 
28.2135 


Cube 
Root. 


9.1458 
9.1498 
9.1537 
9.1577 
9.1617 

9.1657 
9.1696 
9.1736 
9.1775 
9.1815 

9.1855 
9.1894 
9.1933 
9.1973 
9.2012 

9.2052 


Log 


1000 

X 
Recip. 


2.887051 
2.88762; 


2.88874] 
2.88930; 


1.30719 

1.3C 

1.3C 

1.30208 

1.3C 

1.29870 
1.29702 
1.29534 
1.29366 
1.29199 


. 
2415.9 

2419.0 
2422.2 
2425.8 

2428.5 
2431.6 


9.2287 
9.2326 
n .  2:165 
9.2404 

9.2443 


9.2521 
9.2560 


9.1688 

9.2677 
9.2716 
9.2754 


26.2480 
8B.90M 


28.2843    9.2832 
28.3019J  9.2870 

28.3196  :__;„ 

28.3373  9.2948 


9.3025 
9.3063 


. 

9!  3140 
9.3179 


. 

2.89042: 
2.89098 
2.89154; 


1.29032  2434.'. 
1.288661  2437.9 
1.28700)  2441.0 
1.28535'  2444.2 
1.28370  2447.3 


2.89542 

2.89597 
2.89653 


2.89873 
2.89927 


2.90037 
2.90091 
2.90146 

2  .'.it  nit  X) 
2.90255 

2.90309 
2.90363 
2.90417 

2.90472 


2.90580 
2.90634 


. 

2.1)0711 
2.9079-1 


l.: 

1.28041 
1.27877 
1.27714 
1.27551 

1.27389 
.27226 
!  27086 

.20904 
.26743 


.26103 

.2.7.115 


2450.4 
2453.6 
2456.' 
2459.9 
2463.0 

2466.2 
M0B.8 

2472.4 
2475.6 

2478.7 


. 

2488.1 
2491.3 


.25786  2497.6 
"*    2500." 


.25156:  2510.1 

.25000!  2513.3 

.24844!  2516.4 

.24688,  2519.6 

.245.33  2522.7 

.24378  2525.8 

.24224|  2529.0 
.24069  2532.1 

25:55..'} 


Area 


459635 
460837 
462042 
463247 
464454 

465663 
466873 


471730 
472948 
474168 
475389 
476612 

477836 
479062 
480290 
481519 
482750 


485216 
486451 


490167 
491409 
492652 
493897 
495143 

496391 
497641 
498892 
500145 
501399 

502655 

503912 
505171 
50fJ4:-W 
507694 

508958 
510223 
511490 
512758 
514028 


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300                     NATIONAL  TUBE  COMPANY. 

Squares,  Cubes,  Square  Roots,  Cube  Roots,  Logarithms,  Etc. 

(CONTINUED.) 

No. 

Sq. 

Cube. 

Square 
Root. 

Cube 
Root. 

Log. 

1000 
X 
Recip. 

No.  =  Dia 

Circ'm 

Area. 

855~ 

731025 

625026375 

29.2404 

9.4912 

2.93197 

1.16959 

2686.1 

574146 

856 

732736 

627222016 

29.2575 

9.4949 

2.93247 

1.16822 

2689.2 

575490 

857 

734449 

629422793 

29.2746 

9.4986 

2.93298 

1.16686 

2692.3 

576835 

858 

736164 

631628712 

29.2916 

9.5023 

2.93:349 

1.16550 

2695.5 

578182 

859 

737881 

633839779 

29.3087 

9.5060 

2.93399 

1.16414 

2698.6 

579530 

860 

739600 

636056000 

29.3258 

9.5097 

2.93450 

1.16279 

2701.8 

580880 

861 

741321 

638277381 

29.3428 

9.5134 

2.93500 

1.16144 

2704.9 

582232 

862 

743044 

640503928 

29.3598 

9.5171 

2.93551 

1.16009 

2708.1 

583585 

863 

744769 

642735647 

29.3769 

9.5207 

2.93601 

1.15875 

2711.2 

584940 

864 

746496 

644972544 

29.3939 

9.5244 

2.93651 

1.15741 

2714.3 

586297 

865 

748225 

647214625 

29.4109 

9.5281 

2.93702 

1.15607 

2717.5 

587655 

866 

749956 

649461896 

29.4279 

9.5317 

2.93752 

1.15473 

2720.6 

589014 

867 

751689 

651714363 

29.4449 

9.5354 

2.93802 

1.15340 

2723.8 

590375 

868 

753424 

653972032 

29.4618 

9.5391 

2.93852 

1.15207 

2726.9 

591738 

869 

755161 

656234909 

29.4788 

9.5427 

2.93902 

1.15075 

2730.0 

5931C2 

870 

756900 

658503000 

29.4958 

9.5464 

2.93952 

1  14943 

2733.2 

594468 

871 

758641 

660776311 

29.5127 

9.5501 

2.94002 

1.14811 

2736.3 

595835 

872 

760384 

663054848 

29.5296 

9.5537 

2.94052 

1.14679 

2739.5 

597204 

873 

762129 

665338617 

29.5466 

9.5574 

2.94101 

1.14548 

2742.6 

598575 

874 

763876 

667627624 

29.5635 

9.5610 

2.94151 

1.14416 

2745.8 

599947 

875 

765625 

669921875 

29.5804 

9  5647 

2.94201 

1.14286 

2748.9 

601320 

876 

767376 

672221376 

29.5973 

9.5683 

2.94250 

1.14155 

2752.0 

602696 

877 

769129 

674526133 

29.6142 

9.5719 

2.94300 

1.14025 

2755.2 

604073 

878 

770884 

676836152 

29.6311 

9.5756 

2.94:349 

1.13895 

2758.3 

605451 

879 

772641 

679151439 

29.6479 

9.5792 

2.94399 

1.13766 

2761.5 

606831 

880 

774400 

681472000 

29.6648 

9.5828 

2.94448 

1.13636 

2764.6 

608212 

881 

776161 

683797841 

29.6816 

9.5865 

2.94498 

1.13507 

2767.7 

609595 

882 

777924 

686128968 

29.6985 

9.5901 

2.94547 

1.13379 

2770.9 

610980 

883 

779689 

688465387 

29.7153 

9.5937 

2.94596 

1.13250 

2774.0 

612366 

884 

781456 

690807104 

29.7321 

9.5973 

2.94645 

1.13122 

2777.2 

613754 

885 

783225 

693154125 

29.7489 

9.6010 

2.94694 

1.12994 

2780.3 

615143 

886 

784996 

695506456 

29.7658 

9.0046 

2.94743 

1  .  12867 

-.'rs.-i.r, 

616534 

887 

786769 

697864103 

29.7825 

9.60H2 

2.94792 

1.12740 

2786.6 

617927 

888 

788544 

700227072 

29  799:  J 

9.6118 

2  94841 

1.12613 

2789.7 

619321 

889 

790321 

702595369 

29.8161 

9.6154 

2.94890 

1.12486 

2792.9 

620717 

890 

792100 

704969000 

29.8329 

9.6190 

2.94939 

1.12360 

2796.0 

622114 

891 

793881 

707347971 

29.8496 

9.6226 

2.94988 

1.12233 

2799.2 

623513 

892 

795664 

709732288 

29.8664 

9  621  W 

2.95036 

1.12108 

2802.3 

624913 

893 

797449 

712121957 

29.8831 

9.6298 

2.95085 

1.11982 

2805.4 

626315 

894 

799236 

714516984 

29.8998 

9.6334 

2.95134 

1.11857 

2808.6 

627718 

895 

801025 

716917375 

29.9166 

9.6370 

2.95182 

1.11732 

2811.7 

629124 

896 

802816 

719323136 

29.9*33 

9.6406 

2.95231 

1.11607 

2814.9 

630530 

897 

804(10!) 

721734273 

29.9500 

9.6442 

2.95279 

1.11483 

2818.0 

631938 

898 

806404 

724150792 

29.9666 

9.6477 

2.95328 

1.11359 

2821.2 

633348 

899 

808201 

726572699 

29.9833 

9.6513 

2.95376 

1.11235 

2824.3 

634760 

NATIONAL  TUBE  COMPANY.                      301 

Squares,  Cubes,  Square  Roots,  Cube  Roots,  Logarithms,  Etc. 

(CONTINUED.) 

Square 

Cube 

1000 

No.  =  Dia. 

No. 

Sq. 

Cube. 

Root. 

Root. 

Log. 

X 
Recip. 

^irc'm 

Area. 

900 

810000 

729000000 

30.0000 

9.6549 

2.95424 

1.11111 

2827.4 

636173 

901 

811801 

731432701 

30.0167 

9.6585 

2.95472 

1.10988 

2830.6 

637587 

902 

813604 

733870808 

30.0333 

9.6620 

2.95521 

.10865 

2833.7 

639003 

903 

815409 

736314327 

30.0500 

9.6656 

2.95569 

.10742 

2836.9 

640421 

904 

817216 

738763264 

30.0666 

9.6692 

2.95617 

.10619 

2840.0 

641840 

905 

819025 

741217625 

30.0832 

9.6727 

2.95665 

.10497 

2843.1 

643261 

906 

820836 

743677416 

30.0998 

9.6763 

2.95713 

1.10375 

2846.3 

644683 

907 

822649 

746142643 

30.1164 

9.6799 

2.95761 

.10254 

2849.4 

646107 

908 

748613312 

30.1330 

9.6834 

2.95809 

.10132 

2852.6 

647533 

909 

826281 

751089429 

30.1496 

9.6870 

2.95856 

.10011 

2855.7 

648960 

910 

828100 

75-3571000 

30.1662 

9.6905 

2.95904 

1.09890 

2858.8 

650388 

911 

829921 

756058031 

30.1828 

9.6941 

2.95952 

1.09769 

2862.0 

651818 

912 

831744 

758550528 

30.1993 

9.6976 

2.95999 

1.09649 

2865.1 

653250 

913 

883566 

761048497 

30.2159 

9.7012 

2.96047 

1.09529 

2868.3 

654684 

914 

835396 

763551944 

30.2324 

9.7047 

2.96095 

1.09409 

2871.4 

656118 

915 

837225 

766060875 

30.2490 

9.7082 

2.96142 

1.09290 

2874.6 

657555 

916 

83905(5 

768575296 

30.2655 

9.7118 

2.96190 

1.09170 

2877.7 

658993 

917 

SIUSS'.I 

771095213 

30.2820 

9.7153 

2.962437 

1.09051 

2880.8 

660433 

918 

842724 

773620632 

30.2985 

9.7188 

2.96284 

1.08932 

2884.0 

661874 

919 

844561 

776151559 

30.3150 

9.7224 

2.96332 

1.08814 

2887.1 

66*317 

920 

846400 

778688000 

so.asis 

9.7259 

2.96379 

1.08696 

2890.3 

664761 

921 

848241 

781229961 

30.3480 

9.7294 

2.96426 

1.08578 

2893.4 

666207 

922 

850084 

783777448 

30.3645 

9.7329 

2.96473 

1.08460 

2896.5 

667654 

923 

851929 

786330467 

30.3809 

9.7364 

2.96520 

1.08342 

2899.7 

669103 

924 

853776 

788889024 

30.3974 

9.7400 

2.96567 

1.08225 

2902.8 

670554 

925 

855625 

791453125 

30.4138 

9.7435 

2.96614 

1.08108 

2906.0 

672006 

926 

857476 

794022776 

30.4302 

9.7470 

2.96661 

1.07991 

2909.1 

673460 

927 

859329 

796597983 

30.4467 

9.7505 

2.96708 

1.07875 

2912.3 

674915 

928 

861184 

799178752 

30.4631 

9.7540 

2.96755 

1.07759 

2915.4 

676372 

929 

863041 

801765089 

30.4795 

9.7575 

2.96802 

1.07643 

2918.5 

677&31 

930 

864900 

804357000 

30.4959 

9.7610 

2.96848 

1.07527 

2921.7 

679291 

931 

866761 

806954491 

30.5123 

9.7645 

2.96895 

1.07411 

2924.8 

680752 

932 

868624 

809557568 

30.5287 

9.7680 

2.96942 

1.07296 

2928.0 

682216 

933 

870489 

812166237 

30.5450 

9.7715 

2.96988 

1.07181 

2931.1 

683680 

934 

872356 

814780504 

30.5614 

9.7750 

2.97035 

1.07066 

2934.2 

685147 

935 

874225 

817400375 

30.5778 

9.7785 

2.97081 

1.06952 

2937.4 

686615 

936 

876096 

820025856 

30.5941 

9.7819 

2.97128 

1.06838 

2940.5 

688084 

937 

877969 

822656953 

30.6105 

9.7854 

2.97174 

1.06724 

2943.7 

689555 

938 

879844 

825293672 

30.6268 

9.7889 

2  97220 

1.06610 

2946.8 

691028 

939 

881721 

827936019 

30.6431 

9.7924 

2.97267 

1.06496 

2950.0 

692502 

940 

883600 

830584000 

30.6594 

9.7959 

2.97313 

1.06383 

2953.1 

693978 

941 

885481 

833237621 

30.6757 

9.7993 

2.97359 

1.06270 

2956.2 

695455 

942 

887364 

8:35896888 

30.6920 

9.8028 

2.97405 

1.06157 

2959.4 

696934 

943 

889249 

&38561807 

30.7083 

'.(.son: 

2.97451 

1.06045 

2962.5 

698415 

944 

891136 

841232384 

30.7246 

9.8097 

2.97497 

1.05932 

2965.7 

699897 

302                      NATIONAL  TUBE  COMPANY. 

Squares,  Cubes,  Square  Roots,  Cube  Roots,  Logarithms,  Etc. 

(CONTINUED.) 

Square 

Cube 

1000 

No.  =  Dia. 

No 

Sq. 

Cube. 

Root. 

Root. 

Log. 

X 

Recip 

Circ'm 

Area. 

945 

893025 

843908625 

30.740 

9.813;. 

2.9754 

1.0582 

2968.8 

701380 

946 

894916 

84659053C 

30.757 

9.8167 

2.9758 

1.0570 

2971. 

702865 

947 

896809 

84927812,' 

30.7734 

9.8201 

2.9763 

1.0559 

2975. 

704352 

948 

898704 

851971392 

30.7896 

9.8236 

2.9768 

1.05485 

2978.2 

705840 

949 

900601 

854670349 

30.8058 

9.8270 

2.9772 

1.05374 

2981  4 

707330 

950 

902500 

857375000 

30.822 

9.8305 

2.97772 

1.0526 

2984.5 

708822 

951 

904401 

860085351 

30.8383 

9.8339 

2.97818 

1.05152 

2987. 

710315 

952 

906304 

862801408 

30.854o 

9.8374 

2.97864 

1.05042 

2990.8 

711809 

953 

908209 

86552317" 

30.870" 

9.8408 

2.97909 

1.04932 

2993.9 

713306 

954 

910116 

868250664 

30.8869 

9.8443 

2.9795o 

1.04822 

2997  1 

714803 

955 

912025 

870983875 

30.9031 

9.8477 

2.98000 

1.04712 

3000.2 

716303 

956 

913936 

873722816 

SO.  9192 

9.8511 

2.98046 

1.04603 

3003.4 

717804 

957 

915849 

876467493 

30.9354 

9.8546 

2.98091 

1.04493 

3006.5 

719306 

958 

917764 

879217912 

30.9516 

9.8580 

2.9813" 

1.04384 

3009.6 

720810 

959 

919681 

881974079 

30.967" 

9.8614 

2.98182 

1.04275 

3012.8 

732316 

960 

921600 

884736000 

30.9839 

9.8648 

2.9822" 

1.0416" 

3015.9 

723823 

961 

923521 

887503681 

31.0000 

9,8683 

2.98272 

1.04058 

3019.1 

725333 

962 

925444 

890277128 

31.0161 

9.8717 

2.98318 

1.03950 

3022.2 

726842 

963 

927369 

893056347 

31.0322 

9.8751 

2.98363 

1.03842 

3025.4 

728354 

964 

929296 

895841344 

31.0483 

9.8785 

2.98408 

1.03734 

3028.5 

729867 

965 

931225 

898632125 

31.0644 

9.8819 

2.98453 

1.03627 

3031.6 

731382 

966 

933156 

901428696 

31.0805 

9.8854 

2.98498 

1.03520 

3034.8 

732899 

967 

935089 

904231063 

31.0966 

9.8888 

2.98543 

1.03413 

3037.9 

734417 

968 

937024 

907039232 

31.1127 

9.8922 

2.98588 

1.03306 

3041.1 

735937 

969 

938961 

909853209 

31.1288 

9.8956 

2.98632 

1.03199 

3044.2 

737458 

970 

940900 

912673000 

31.1448 

9.8990 

2.98677 

1.03093 

3047.3 

738981 

971 

942841 

915498611 

31.1609 

9.9024 

2.98722 

1.02987 

3050.5 

740506 

972 

944784 

918330048 

31.1769 

9.9058 

2.98767 

1.02881 

3053.6 

742032 

973 

946729 

921167317 

31.1929 

9.9092 

2.98811 

1.02775 

3056.8 

743559 

974 

948676 

924010424 

31.2090 

9.9126 

2.98856 

1.02669 

3059.9 

745088 

975 

950625 

926859375 

31.2250 

9.9160 

2  98900 

1.02564 

3063.1 

746619 

976 

952576 

929714176 

31.2410 

9.9194 

2.98945 

1.02459 

3066.2 

748151 

977 

954529 

9325748-33 

31.2570 

9.9227 

2.98989 

1.02354 

3069.3 

749685 

978 

956484 

935441352 

31.2730 

9>>m 

2.99034 

1.02249 

3072.5 

751221 

979 

958441 

938313739 

31.2890 

9.9295 

2.99078 

1.02145 

3075.6 

752758 

980 

960400 

941192000 

31.3050 

9.9329 

2.99123 

1.02041 

3078.8 

754296 

981 

962361 

944076141 

31.3209 

9.9363 

2.99167 

1.01937 

3081.9 

755837 

982 

964324 

946966168 

31.3369 

9.  9:  51  1C, 

2.99211 

1.01833 

3085.0 

757378 

983 

966289 

949862087 

31.3528 

9.9430 

2.99255 

1.01729 

3088.2 

758922 

984 

968256 

952763904 

31.3688 

9.9464 

2.99300 

1.01626 

3091.3 

760466 

985 

970225 

955671625 

31.3847 

9.9497 

2.99344 

1.01523 

3094.5 

762013 

986 

972196 

958585256 

31.4006 

9.9531 

2.99388 

1.01420 

3097.6 

763561 

987 

974169 

961504803 

31.4166 

9.9565 

2.99432 

1.01317 

3100.8 

765111 

988 

976144 

964430272 

31.4325 

9.9598 

2.99476 

1.01215 

3103.9 

766662 

989 

978121 

967361669 

31.4484 

9.9632 

2.99520 

1.01112 

3107.0 

768214 

',                                                                                                                                  _ 

NATIONAL  TUBE  COMPANY. 


Squares,  Cubes,  Square  Rootst  Cube  Roots,  Logarithms,  Etc. 

(CONTINUED.) 


990 
991 


995 
996 
997 


Sq. 


Cube. 


980100  970299000 

982081  973242271 

984064  976191488 

986049!  979146657 

988036  982107784 

990025  985074875 

992016  988047936 

994009  991026973 

996004  994011992 


Square 
Root. 


31.4643 
31.4802 
31.4960 
31.5119 
31. £ 

31.5436 
31.5595 
31.5753 
31.5911 
31.6070 


Cube 
Root. 


9.9733 
9.9766 


9.9866 
9.9900 
9.9933 
9. 9967 


Log 


2.99564 
2.99607 
2.99651 
2.99695 


Recip. 


1.01010 

1.00 

1.00806 

1.00705 

1.00604 


2.99782  1.00503 
.00402 
2.99870  1.00301 
2.99913  1.00200 
2.999571  1.00100 


Circ'm 


3110.2 
3113.3 
3116.5 
3119.6 
3122.7 

3125.9 
3129.0 
3132.2 
3135.3 
3138.5 


774441 

776002 


INDEX. 


NATIONAL  TUBE  COMPANY. 


INDEX  TO  TABLES  OF  STANDARD 

DIMENSIONS  OF  TUBULAR 

GOODS. 


Axle  bearings,  bushing  forgings  for 

Bearings,  bushing  forgings  for 

Bedstead  tubing       ...... 

Bends,  offset  pipe  bends     ..... 

' '        pipe  bends 

"        stock  pipe  bends 

Black  standard  weight  pipe     . 

Boiler  tubes,  cold  drawn 

"          "        special  sizes         .... 

"          "        standard         ..... 
Boiler  shells,  seamless      ..... 
Bowl  forgings  for  separators        .... 
Bushing  forgings  for  axle  bearings 

Caps  for  carbonic  acid  cylinders. 

Carbonic  acid  cylinders  .... 

Casing,  couplings  for  ..... 

"          lap-welded 

Cold  drawn  tubes,  description  and  uses  of 
"        ."      tubing  for  boilers,  locomotives,  etc. 
"         "       tubes,  tables  of  . 

Collar  flanges,  cast-iron     ..... 
Converse  lock  joint  fittings  . 

"        patent  lock  joint  for  pipe 
Couplings  for  drive  pipe     ..... 
"  "    line  pipe  .... 

"  "     regular  casing      .... 

"  "     steam,  gas  and  water  pipe 

"  "    tubing 

Cylinders,  special  8"  seamless 

standard  5"  and  8"  seamless 
"  standard  5"  lap- welded 

"  3"  to  20"  seamless 


PAGE 
.  91 

.  91 
.  14 

.  44 
41-44 

.  43 
2 

.  73 
.  13 
10,11 
.  90 

.  91 
.  91 

.  90 
83-89 

.  16 
6,  7 

.  72 
.  73 
77-81 
21,25 
28-32 
.  27 

.  18 
.  17 

.  16 
.  15 

.  18 
.  86 
83-85 
.  89 
87,88 


308  NATIONAL  TUBE  COMPANY. 

Deflections  of  National  trolley  poles        .         .  46-67 

Double  extra  strong  pipe        .  .         .         .        .     4 

Double  riveted  pipe  flanges       .          .         .         .        23,  25 

Drawn  tubing,  uses  of 70-72 

Drive  pipe 8 

"        "  couplings     .          .         .         .         .         .         .18 

Extra  strong  pipe 3 

Fittings,  Converse  joint  fittings             .         .         .  28-32 

"      Matheson      "         "                ...  33-36 

Flanges,  cast-iron  collar 21,  25 

"          ' '      "    double  riveted       ...  23,  25 

"          "       "     single        "               ...  22,  25 

"          "       "     lugged  for  special  light  pipe  19,25 

"          "       "        "        pump  column      .         .  20,25 

"     Master  Steam  Fitters' standard             .  .       26 

"     solid  welded 24,25 

"     threaded,  cast-iron       .....       26 

Floats,  seamless 90 

Flush  joint  pipe  and  tubing 9 

Franklin ite  locomotive  boiler  tubes            .         .  .12 

Galvanized  standard  weight  pipe     ....         2 
Gas  pipe  couplings     .         .         .        _.  .         .15 

Heating  surface  of  pipe  .         .         .         .         .         5 

Hot  finished  seamless  tubes  ....      74-76 

Hydraulic  forgings  ...  90,  91 

Joint,  Converse  lock 27 

"      Matheson 33 

Ivap-welded  casing 6 

"        "         cylinders 89 

"         "  pipe,  special  light  with  flanges         .      19,  25 

"  "      with  collar   flanges       .         .         21,25 

"         "  "         "     double  riveted  flanges     .     23,25 

"        "  "        "      single  riveted  flanges           22,25 

"         "  "        "      Converse  lock  joint        .         .  27 


NATIONAL  TUBE  COMPANY. 


L,ap-welded  pipe  with  Matheson  joint     ...       33 
"          "          "         "     solid  welded  flanges  .     24,25 

"          "        pump  columns  and  flanges  .         .       20 

"          "        tuyere  pipe       .          .          .          .          .          .14 

Large  size  O.  D.  pipe .9 

Light  lap-welded  pipe  with  cast-iron  lugged  flanges  19,  25 
Line  pipe        .  .......         8 

Line  pipe  couplings  .         .         '          .         .         .17 

Lock  joint,  Converse 27 

Locomotive  boiler  tubes,  cold  drawn         ...       73 

"  "         "         lap -welded,  special  brands      12 

Lugged  flanges,  cast-iron  for  special  light  pipe      19,    25 

"  "          "       "     pump  column       .          .  20,    25 

Master  Steam  Fitters'  standard  pipe  flanges     .         .       26 

Matheson  joint  fittings 34-36 

"          patent  pipe  joint     .....       33 
Mechanical  tubes,  cold  drawn     .         .         .         .         .73 

National  trolley  poles 46-67 

Oil  well  tubing 8 

Pipe  bends 41-44 

"       couplings,  see  couplings 

"       flanges,      see  flanges 

"  joint,  flush  ,  .  .  .  .  .  .9 

Projectile  forgings 91 

Protecting  caps  for  carbonic  acid  cylinders  .  .  90 

Pump  columns  and  pump  column  flanges  .  .  20 

Radii  for  pipe  bends         ......       42 

Riveted  pipe  flanges 22,  23,  25 

Salamander  locomotive  boiler  tubes         ...       12 

Seamless  boiler  shells 90 

"        cold  drawn  boiler  tubes  ...       73 

"      tubes          .          .         .         .      77-81 

cylinders 83-88 

"  "          illustrations  of     .         .         .     83,87 


310 


NATIONAL  TUBE  COMPANY. 


Seamless  cylinders  3"   to  20"  diameter  .         87,  88 

"          drawn  tubing,  description  and  uses  of      70-72 

floats 90 

1 '          hot  finished  tubes  .         .         .  74-76 

tubular  goods  ....      70-91 

Separator  bowl  and  tubular  forgings  91 

Shrapnel  forgings 90 

Single  riveted  pipe  flanges       ....         22,  25 

Solid  welded  flanges 24,    25 

Special  8"  seamless  cylinders  for  carbonic  acid        .       86 
Special  light  lap -welded  pipe  with  flanges  .         .     19,  25 

' '      sizes  of  boiler  tubes 13 

"      steel  lap-welded  pipe  with  Converse  joint    .  27 
"        "      "          "          "          "     Matheson  joint       33 

Standard  boiler  tubes 10,  11 

"        couplings  for  drive  pipe       .         .         .         .18 
"  '*  "  line  pipe     ....       17 

"  "  "  regular  casing         .         .         .16 

"  "  steam,  gas  and  water  pipe      15 

"  "  "  tubing         ....       18 

' '        double  extra  strong  pipe        .         .         .         .4 

"        drive  pipe 8 

"        extra  strong  pipe  .         .         .         .         .3 

"        line  pipe    .......       8 

"        oil  well  tubing      .         .         .         .         .         .8 

"        seamless  cylinders  5"  and  8"     .         .         83-85 

' '        weight  pipe,  black  and  galvanized      .  .     2 

Steam  pipe  couplings       ......       15 

Stock  pipe  bends 43 

Swelled  tube  ends 37 

Threaded  cast-iron  pipe  flanges           .         .         .  .26 

Trolley  pole  dimensions  and  deflections.          .  46-67 

Tubes,  bent 41 

"        seamless  cold  drawn     ....  77-81 

"              "            hot  finished     ....  74-76 

' '        special  brands  locomotive  boiler  tubes  .       12 

"             "       sizes  of  boiler  tubes     .  .   13 


NATIONAL  TUBE  COMPANY. 


Tubes,  standard  boiler  tubes  ....  10 
with  upset  ends 37-40 

Tubing,  bedstead 14 

"  couplings  for  .  .  .  .  .  .18 

"  oil  well 8 

"  seamless  cold  drawn  for  boilers,  etc  .  .  73 

Tubular  forgings  for  separators       .         .         .         .91 

Tuyere  pipe 14 

Upset  and  swelled  tube  ends  ....  37 
tube  ends 37-40 

Valve  protecting  caps  for  carbonic  acid  cylinders          90 

Water  pipe  couplings,  black  and  galvanized  .  .  15 
Welded  flanges,  pipe  with  ....  24-25 
Working  barrels 82 


NATIONAL  TUBE  COMPANY. 


INDEX  TO  USEFUL  INFORMATION. 


PAGE 

Absolute  temperature        ......   164 

"       zero 164 

Acid  Bessemer  process       ......  201 

"    open  hearth  process 202 

Acids  in  feed-water 96 

Adiabatic  compression  and  expansion  of  air,  165, 166,  172 
After-coolers  for  air  compressors  .         .         .       176 

Air  164-192 

"    adiabatic  compression  and  expansion  of,  165, 166,  172 
"    Boyle's  law  for  .         .         .         .         .         .  164 

"    Charles'  and  Gay  Lussac's  law  for  .         .       164 

"    composition  of 164 

"    compression  of 165-171 

"    compressors          ......    175-180 

"  "        after-coolers  for         .         .         .         .176 

"  "       compound  ....     175-177 

"  "        capacity  of 180 

efficiency  of,  at  different  altitudes  178-179 
"  ' '        horse-power  required  for     .         .         .   180 

"  "        inter-coolers  for     .         .         .  175-178 

"  "        saving  due  to  compounding  .         .  177 

"    corrosion  caused  by  air  in  water    ...         96 

"    expansion  of 165,  166 

"    flow  of,  through  pipes      ....         183-192 

"      "       "          "        orifices 182 

' '    in  feed  water 96 

"    isothermal  compression  and  expansion  of      167,  172 
"    pressure  curves  of  .....   172 

"    resistance  to  flow  by  valves,  etc.      .         .         .       190 
"    saturated  with  vapor  .....  181 

"    specific  heat  of         ......       165 

'     weight  of 164,  181 

"    work  of  compression        ....         166-170 
Analysis  of  water        .......    98 


NATIONAL  TUBE  COMPANY. 


Basic  Bessemer  process 201 

' '     open  hearth  process 202 

Bearing  value  of  rivets  .         .         .          .         .       228 

Bending  moments  of  beams,  etc .        .         .          .    212,213 

Bessemer  process  for  making  steel          .         .          .       201 
Boilers,  acid  in  feed-water          .          .          .          .         .96 

"         air  in  feed-water        .         .         .         .          .         96 

"          chimneys  for.         ....  158-161 

"          commercial  horse-power  of          .         .         .     152 
"          corrosion  in     ......     96-98 

"          evaporation,  unit  of    .         .         .         .         .     152 

"          factors  of  evaporation,  table  of      .         .  137 

"          feed- water  heaters       .         .         .         .         .154 

"          feed  water,  impurities  in          .         .         .      95-98 
"          grease  and  oil  in .         ....          96-98 

"          horse-power  of        ....  152,  153 

"          impurities  in  feed-water       .         .         .         85-98 

"          incrustation 95-98 

lime  in  feed-water       ....    95.97,98 

"          moisture  in  steam  ....  153 

"          mud  in  feed-water     .         .         .         .  95,    97 

*    "          non-conducting  coverings  .         .         .     147 

«'          oil  and  grease  in 96-98 

"          power  of  boilers  ....     152,153 

"          pressure,  safe  working  .         .  157,  222 

prevention  of  corrosion          .         .         .         95-98 

"  scaling        .         .         .95,  97,  98 

salt  in  feed- water 96 

strength  of     .          .         .         .  157,  218,  222 

"          treatment  of  impure  feed-water    .          .          95-98 
"          unit  of  evaporation  ....        152 

Bolts,  strain  in 244 

' '      strength  of 243 

' '      weight  of 231 

Boyle's  law  for  air  and  gas        .....  164 

Brake  horse-power 152 

Brass  plate,  weight  of  .  .         .236,  237 

British  thermal  unit        ....  .       134 


NATIONAL  TUBE  COMPANY. 


Burners,  services  for          ......  196 

Bursting  pressure  of  pipes,  etc.       .         .         .        217-223 

Capacity  of  air  compressors 180 

"        "   cisterns  and  tanks .       ....       122 

"        "  cylindrical  vessels  ....  119 

"        "   pipes  .         .         .         .  .118 

"        "   rectangular  tanks  ....  123 

Cementation  process  for  making  steel .  .         .       200 

Charles'  and  Gay  Lussac's  law  ....  164 

Chimneys  for  boilers       .....       158,  161 

Circle,  properties  of 260 

table  of,  by  eighths  .         .         .         .271 

"      "    from  1  to  1000          .         .         .         .281 

Cisterns,  capacity  of 122 

Commercial  horse-power  of  boilers  .         .         .152 

Composition  of  air          ......       164 

"  of  water         .         .         .         .         .         .94 

Compound  air  compressors     ....       175,  177 

Compound  units,  Metric  and  U.  S 253 

Compressors  of  air 165,  171 

Compressors  for  air  .....   175,  186* 

Condensation  of  steam  in  pipes      ....       149 
Conversion  table,  Metric  and  U.  S.  .         .         .  251 

Corrosion  in  boilers  and  tubes         .         .         .         96,    98 

Cosines,  table  of 268 

Cotangents 270 

Coverings  for  steam  pipes 147 

Cubes  of  numbers,  table  of.            .         .         .         .       281 
Cylinder  heads,  strength  of 223 

Decimals  of  an  inch  for  each  1-64  ....       235 
"          "a  foot  for  each  inch       ....  235 

Deflection  of  beams 212 

"  pipes  212-217 

Density  of  water 94 

Depth  of  pump  suction     ......  131 

Discharge  of  water  from  orifices  and  nozzles          .       124 


NATIONAL  TUBE  COMPANY. 

315 

Discharge  of  water  from  pipes   .  102,  105,  107,   108,  113 

Dry  steam,  definition  of          ... 

.       134 

Effective  head  for  water  pipes  . 

.  112 

"        thickness  of  pipe     . 

.       217 

Efficiency  of  bolts     

.  242 

"           "    air  compressors 

.       178,   179 

Elastic  limit,  definition  of         ... 

.  210 

"          "of  materials 

.      206 

Elastic  material         

.  210 

Elasticity,  modulus  of             ... 

206,  210 

Electrical  equivalents        .... 

.     253-256 

Equivalents,  mechanical,  electrical  and  heat 

249,  253-256 

"              trigonometrical     . 

.  262 

Evaporation,  unit  of       .... 

152 

Expansion  of  air        

.    165,  166 

Factor  of  safety      ..... 

.       209 

Factors  of  evaporation,  table  of 

.  137 

Feed-water  heaters          .... 

.       154 

Feed-  water,  impurities  in 

95-98 

Fifth  roots  and  fifth  powers 

.       277 

Flow  of  air  in  pipes            .... 

.     183-192 

"     "  gas  "     " 

194,  195 

"     "  steam  in  pipes       .... 

.     142-147 

"     "  water  "      "        .             101,105,  107, 

110,  112,  113 

"     "  air  through  orifices 

.  182 

"     "  gas      " 

194,  195 

"     "  steam  "                           ... 

.    140,  141 

"     "  water  "              "... 

.       124 

Frictional  heads        

.     110-112 

Frost,  trouble  from,  in  gas  pipes 

194,  195 

Gas            

.     194-198 

"  flow  of,  in  pipes         .... 

194,  195 

4  '  frost,  trouble  from       .... 

.  195 

'  '  holders,  weight  of     . 

197 

"  services  for  burners     .... 

.  196 

'  '  vapor  contained  in 

.       196 

, 

NATIONAL  TUBE  COMPANY. 


Gauges,  standard  ......       234 

Gay  lyussac's   law 164 

Grease  in  boilers 96-98 

Head,  definition  of  101,  107 

"      effective       .......       112 

frictional 110-112 

"       of  water  for  given  discharge         .         .         .       102 

table  of  pressures  due  to  .         .         .99 

Heads,  strength  of  cylinder  ....       223 

Heat  equivalents 249,  253-256 

<l     intensity 253 

' '    loss  from  steam  pipes         ....    149,  150 

"     mechanical  equivalent  of        ....       164 

"     specific  heat  of  gases        .  ...  165 

"  "        "  steam    .          .         .  •  .       134 

Horse-power,  definition  of         ....    151,  152 

' '  equivalents  of  .         .         .         .         .       249 

"  of  boilers 152,  153 

of  engines         .         .         .         .151,  154 

of  flowing  water  .         .         .         .   126 

"  of  water-wheels         ....       126 

"  required  for  air  compressors         .         .   180 

House-service  pipes       .         .         .         .         .         .        113 

Impurities  in  water            ...                   .  95-98 

Incrustation  of  boilers  and  pipes            .         .  95-98 
Indicated  horse-power                .....    151 

Inertia,  moment  of.                ....  211,  213 

Inter-coolers  for  air  compressors       .         .         .  175-178 

Internal  bursting  pressure     ....  217-223 

Iron  and  steel 200-208 

"      "      "  tenacity  of  at  different  temperatures  207, 208 

Iron,  weight  of  plate 236-239 

Isothermal  compression  and  expansion  of  air,  167, 172 


Latent  heat  of  steam 
Lime  in  feed-water 
Logarithms,  table  of 


134 


95,  97, 


281 


NATIONAL  TUBE  COMPANY. 


Mathematical  tables 267 

Measurement  of  water       .         .         .         .         .         .   126 

Measures  ....  ...  246 

Metric  System  of 249 

Measure  of  work  and  power  ....  249 

Mechanical  equivalents  ....  249,  253-256 
Mechanical  equivalent  of  heat  ....  164 

Mensuration 258-261 

Metric  conversion  tables  .....  251 
Metric  system  of  weights  and  measures  .  .  .  249 

Modulus  of  elasticity 206,  210 

Modulus  of  section,  definition  of  ....  213 

"  "  table  of  ....  211 

Moisture  in  steam 153 

Moment  of  inertia,  definition  of         ....  213 

"       "        table  of  ....       211 

Mud  in  feed-water 95,    97 

Non-conducting  coverings         .....  147 

Nuts,  size  of 232,  233 

"     weight  of 231-233 

Oil  in  boilers          .... 


Pelton  water-wheel 

Pillars,  strength  of  wrought  iron  . 

Pipe,  effective  thickness  of 

"     hangers  for 

"     sag  of 

"     equivalents    ..... 
Pipes,  flow  of  air  in   .         .         .         .         . 

"          "    "  steam  in  .         .         . 

"    "water  in      .          .         103,104, 

"     relative  discharge  of  steam  . 

"         "  water        .. 

"     water  capacity  of  ... 

Plastic  material 
Plates,  weight  of 
Polygons,  regular 


126,   127 

.         .       224 

217 

216 

217 

.         114,146 

.    183-192 

.         .       142 

107,108,113 

.         .       146 

..  114 

..       118 

210 

236-239 
259,  260 


NATIONAL  TUBE  COMPANY. 


Power  of  boilers, 152,  153 

"        "  engines 151,154 

"  water  fall 125 

"      "     wheels 125-127 

required  to  raise  water        ....       130 

Powers,  fifth 277 

' '  second  and  third     .         .         .         .         .       281 

Pressure  curves  of  air         ......  172 

"        internal  bursting     ....        217-223 

' '        of  water  column 94 

"        under  different  heads      ....         99 

Pressures  safe  for  boilers  ....  157,    222 

"        safe  for  cast  iron  pipes  .         .         .       115 

Prevention  of  corrosion  and  incrustation  .         95-98 

Properties  of  the  circle 260 

"          "  saturated  steam  .         .         .   136,   139 

Pump  suction ,  depth  of 131 

Pumping  hot  water 131 

Pumps  and  pumping  engines          ....       130 

Regular  polygons 259,  260 

Relative  discharging  capacities  of  pipes         .         .114 

Resistance  to  flow  by  bends,  etc .       .         .         .  144,  190 

Rivets,  strength  of 228 

weight  of 230 

Roots,  table  of  fifth 277 

"  "     "  square  and  cube         ....  281 

Safety  factors 209 

Safe  pressures  for  cast-iron  pipes       .         .         .         .115 
Safe  working  pressures  in  boilers  .         .         .       157 

Sag  of  pipe 217 

Salt  in  feed -water 96 

Saturated  steam,  definition  of  ....   134 

properties  of         .          .         .        136,139 

Screw-threads  .  .  240-242 

Services  for  gas  burners.        .         .         .         .'"-'•-.       196 

Shearing  strength  of  materials  .         .  .   206, 210 

"  rivets  228 


NATIONAL  TUBE  COMPANY. 

-^ 

319 

Sheet  metal,  weight  of 

.     236-239 

Sines,  table  of        

.       267 

Size  of  nuts       

.     232,  233 

Solids,  volumes  of           .         . 

.       261 

Specifications  for  steel      .... 

202 

Specific  gravity  of  steam        .... 

.       135 

Specific  heat  of  air              .... 

.  165 

"          "      "  steam    

.       134 

Square  roots,  table  of           .         .         . 

.  281 

Squares  of  numbers,  table  of           ... 

.       281 

Standard  gauges        

.  234 

"         screw-threads           .... 

240-242 

specifications  for  steel 

.  202 

Steam  and  steam  apparatus 

134-161 

condensation  in  pipes 

149 

4  '        coverings  for  steam  pipes 

.       147 

"        dry,  definition  of   . 

134 

"        factors  of  evaporation,  table  of 

.       137 

feed-water  heaters 

145 

'  '        flow  of  from  orifices 

140,  141 

"     "     in    pipes 

142-147 

"        heat  loss  from  pipes 

149,  150 

"        horse-power  of  boilers 

152,  153 

"            "        "       "   engines 

151,154 

"        latent  heat  of         .... 

134 

"        moisture  in         ..... 

134,  153 

"        non-conducting  coverings 

147 

'  '        pipe  coverings           .         .         . 

147 

"            "    equivalents 

146 

'  '        power  of  boilers         .... 

152,  153 

"        "  engines 

151,  154 

"        properties  of  saturated 

136,  139 

*'        resistance  to  flow  by  bends,  etc    . 

.     144 

"        safe  working  pressures  in  boilers     . 

157 

"        saturated,  definition  of 

.     134 

'  '          table  of  properties  of 

.  136,  139 

'  '        specific  gravity  of                . 

.       135 

heat  of     . 

.  134 

—  —  J 

320 


NATIONAL  TlTBE  COMPANY, 


Steam,  super-heated,  definition  of  ...       134 

"  "         "        example  of        ....  153 

unit  of  evaporation 152 

"        wet,  definition  of 134 

"  "    example    " 153 

Steel 200-208 

"      properties  of        ......       206 

"       specifications  for 202-205 

"      tenacity  of,  at  different  temperatures          207,  208 

"      weight  of  plate 236-239 

Strain 209 

Strain  in  bolts 244 

Strength  of  boilers  ....       157,  218,  222 

"  bolts 243 

"         "  cylinders  against  bursting     .         .       217-223 

"         "  cylinder  heads  ....         223 

"         "  iron  and  steel  at  high  temperatures    207,  208 

"materials         .A      *^-      rf  /    •     204-208 

'•  riv€ts          J&*  'Vfr-**^*^  .         .       228 

"  <pfy£&*~*^.         ....    213-227 

"         "  wrought  iron  pillars  .         .         .       224 

Stress 209 

Suction,  depth  of 131 

Superheated  steam,  definition  of        ...  134 

"  "        example  of       ....      154 

Tangents,  table  of 269 

Tanks,  capacity  of 122,  123 

Temperature  conversion  formula            .         .  .       253 

Tenacity  of  metals  at  different  temperatures     .  .   207 

Treatment  of  impure  feed -water     .         .         .  95-98 

Triangles,  solution  of         .....  264-266 

Trigonometry         .         .    .      .         .         .         .  262-266 

Unit  of  evaporation  ......  152 

«  "  work 151 

"  working  strength,  definition  of  .  .  .  209 
"  shearing  "  "  210 

Units,  compound,  Metric  and  U.  S.  .         .         .  253 


NATIONAL  TUBE  COMPANY. 


Vapor  contained  in  air 181 

a  1QA 

gas  ..••••  ivv 
Velocity  of  discharge  .  .  .  .  101,  105,  107 
Vessels,  capacity  of  cylindrical  .  .  .  .119 
Volumes  of  solids 261 

Water •  94-131 

'  *  acids  in  feed-water 96 

"  analysis  of 98 

"  capacity  of  cisterns  and  tanks  .  .  .  122 
"  "  "  cylindrical  vessels  .  .  .  119 

"  "  "  pipes  .....  118 

"  "  "  rectangular  tanks  .  .  .  123 

composition  of 94 

' '  depth  of  suction 131 

4 '  diameter  of  pipe  for  given  discharge  .  103-109 

discharge  from  orifices  and  nozzles  .  124 

"     pipes  102,105,107,108,113 

"  "  "      "        relative     .         .         .        114 

"  effective  head 112 

"  flow  of ,  in  pipes  .  101,105,107,110,112,113 
"  "  "  "  house  service  pipes  .  .  .  113 

"  frictional  heads 110 

' '  grease  and  oil  in  boilers  ....  96-98 
' '  greatest  density  of  .....  94 

'  head,  definition  of  .  .  .  101,107 

"  "in  feet  for  given  discharge  .  .  .  102 
11  "  table  of  pressures  due  to  ...  99 
"  horse  power  of  flowing  water  .  .  126 

"  "  "  "  water-wheels  .  .  .  126 

' '  impurities  in  .  .  .  .  .  95-98 

"  lime  in  feed-water  .  .  .  .  95,  97,  98 
( '  measurements  of  ......  129 

"  miners'  inch 129 

"  mud  in  feed -water 95 

4 '      oil  and  grease  in  boilers        ....  96-98 

"      power  of  water  fall  .....  125 

11     "      "     wheels.          .         .         .         125-127 


4 


NATIONAL  TUBE  COMPANY. 


Water,  power  required  to  raise  water          .         .         .   130 

"      pressure  of  water  column   ....         94 

"        under  different  heads          .         .         .99 

pressures,  safe  for  cast-iron  pipes       .         .       115 

prevention  of  corrosion  and  incrustation   .     95-98 

pump  suction,  depth  of        .         .         .         .131 

pumping  hot  water        .         .          •        .         .131 

"      pumps  for  water 130 

"      relative  discharging  capacities  of  pipes  .         .   114 

' '      salt  in  feed-water 96 

"      suction,  depth  of 131 

tabular  view   of  troubles,  etc. ,  caused  by  im- 
purities in  feed-water         ....       97 
treatment  of  impure          ....      95-98 
"      velocity  of  discharge   .         .         .         101,  105,107 
"      wheels  and  motors    ....  125-127 

'*      weight  of      .......       94 

"in  pipes 121 

Weight  of  air 164,    181 

"      "  bolts  and  nuts  ....  231 

"  rivets 230 

"      "  sheet  and  plate  metal          .         .         .  236 

"      "  water  .         .         .         .         .         .94 

' in  pipes      .         .         .*  .         .121 

Weights  and  measures 246 

"     of  gas-holders 197 

' '    Metric  system  of 249 

Wet  steam,  definition  of 134 

"        example  of 154 

Work,  definition  of  151 

"        unit  of        .......        151 

Work  of  compression  of  air         ....    167,  170 

Working  strength,  definition  of      ....        209 


—  J  —  —  _ 

TT 


2 

§ 


5-    «i 


£ 

i 


YA  03  i 


800375 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


